Ok. Did some digging. People conducting private sales of firearms via internet is pretty common. Armslist and Gunbroker are the two most popular sites for that kind of thing. Also, most gun forums have a section for want to buy/want to sell ads. Sites like these are monitored by staff to ensure no illegal shenanigans happen (plus the ATF routinely visits these sites to make sure everything is on the up-and-up).
Regarding the lack of background checks, Federal law states that when purchasing a firearm from a licensed dealer, you have to fill out Form 4473 which is a legal document that will include name, social security number, make/model/serial number of the weapon, etc. Additionally, the buyer also has to have his SSN run through the National Instant Criminal Background Check System or NICS upon which the dealer will be told whether or not the buyer is eligible to own a firearm under law. Falsifying information on a 4473 is punishable by five years in prison plus fines. Federal Firearms License holders (FFLs; the gun dealers) are required to maintain records of these forms in a bound book for a minimum of 20 years, must produce said records upon ATF request if the request is made in the course of a criminal investigation, and must surrender these records upon leaving the firearms business. State and local laws vary, of course, but the Federal laws are the minimum. Additionally, sites like Gunbroker require any cross-state sales to be shipped through FFLs as further insurance that the transaction is legal.
Private sales (non-FFL holders) do not require a 4473; however, if someone sells guns for a living they must have an FFL.
en.wikipedia.org/wiki/National_Instant_Criminal_Background_Check_Systemen.wikipedia.org/wiki/Form_4473en.wikipedia.org/wiki/Federal_Firearms_LicenseArmor Piercing rounds are a trickier subject. From Title 18 United States Code Chapter 44, Paragraph 44 Section 17:
(17)
(A) The term “ammunition” means ammunition or cartridge cases, primers, bullets, or propellent powder designed for use in any firearm.
(B) The term “armor piercing ammunition” means—
(i) a projectile or projectile core which may be used in a handgun and which is constructed entirely (excluding the presence of traces of other substances) from one or a combination of tungsten alloys, steel, iron, brass, bronze, beryllium copper, or depleted uranium; or
(ii) a full jacketed projectile larger than .22 caliber designed and intended for use in a handgun and whose jacket has a weight of more than 25 percent of the total weight of the projectile.
(C) The term “armor piercing ammunition” does not include shotgun shot required by Federal or State environmental or game regulations for hunting purposes, a frangible projectile designed for target shooting, a projectile which the Attorney General finds is primarily intended to be used for sporting purposes, or any other projectile or projectile core which the Attorney General finds is intended to be used for industrial purposes, including a charge used in an oil and gas well perforating device. In a nutshell, commercially manufacturing and commercially importing AP rounds, as defined, is illegal except in certain cases. 18 U.S.C. Chapter 44 Paragraph 922, section 7
It shall be unlawful
(7) for any person to manufacture or import armor piercing ammunition, unless—
(A) the manufacture of such ammunition is for the use of the United States, any department or agency of the United States, any State, or any department, agency, or political subdivision of a State;
(B) the manufacture of such ammunition is for the purpose of exportation; or
(C) the manufacture or importation of such ammunition is for the purpose of testing or experimentation and has been authorized by the Attorney General;
(8) for any manufacturer or importer to sell or deliver armor piercing ammunition, unless such sale or delivery—
(A) is for the use of the United States, any department or agency of the United States, any State, or any department, agency, or political subdivision of a State;
(B) is for the purpose of exportation; or
(C) is for the purpose of testing or experimentation and has been authorized by the Attorney General; [1]
Punishment for breaking this law as detailed in 18 U.S.C. Chapter 44 Paragraph 929
(a)
(1) Whoever, during and in relation to the commission of a crime of violence or drug trafficking crime (including a crime of violence or drug trafficking crime which provides for an enhanced punishment if committed by the use of a deadly or dangerous weapon or device) for which he may be prosecuted in a court of the United States, uses or carries a firearm and is in possession of armor piercing ammunition capable of being fired in that firearm, shall, in addition to the punishment provided for the commission of such crime of violence or drug trafficking crime be sentenced to a term of imprisonment for not less than five years.
(2) For purposes of this subsection, the term “drug trafficking crime” means any felony punishable under the Controlled Substances Act (21 U.S.C. 801 et seq.), the Controlled Substances Import and Export Act (21 U.S.C. 951 et seq.), or chapter 705 of title 46.
(b) Notwithstanding any other provision of law, the court shall not suspend the sentence of any person convicted of a violation of this section, nor place the person on probation, nor shall the terms of imprisonment run concurrently with any other terms of imprisonment, including that imposed for the crime in which the armor piercing ammunition was used or possessed.
Basically, you illegally use AP rounds and you're looking at 5 years plus whatever else you get convicted of.
Note the legal definition of armor piercing round is restricted to handgun use. Most rifles will defeat armor commonly worn by police using regular bullets.
Below is a list of rounds classified by ATF as AP.
"bullet KTW AMMUNITION, all calibers. (Identified by a green coating on the projectile)
bullet ARCANE AMMUNITION, all calibers. (Identified by a pointed bronze or brass projectile)
bullet THV AMMUNITION, all calibers. (Identified by a brass or bronze projectile and having a headstamp containing the letters SFM and THV)
bullet CZECHOSLOVAKIAN manufactured 9mm Parabellum (Luger) ammunition having an iron or steel core. (Identified by a cupronickel jacket and headstamp containing a triangle, star and dates 49, 50, 51, or 52. The bullet is attracted to a magnet)
bullet GERMAN manufactured 9mm Parabellum (Luger) having an iron or steel bullet core. (Original packaging is marked Pisolenpatronen 08 m.E. May have black colored bullet. This bullet is attracted to a magnet)
bullet MSC AMMUNITION, Caliber .25. (Identified by a hollow point brass bullet. NOTE: MSC ammunition Caliber .25 identified by a hollow point copper bullet is not armor piercing)
bullet BLACK STEEL ARMOR PIERCING AMMUNITION, All Calibers, as produced by National Cartridge, Atlanta, Georgia.
bullet BLACK STEEL METAL PIERCING AMMUNITION, All Calibers, as produced by National Cartridge, Atlanta, Georgia.
bullet 7.62mm NATO AP (Identified by black coloring in the bullet tip. This ammunition is used by various NATO countries. The U.S. military designation is M61 AP)
bullet 7.62mm NATO SLAP (identified by projectile having a plastic sabot around a hard penetrator. The penetrator protrudes above the sabot and is similar in appearance to a Remington accelerator cartridge)
bullet PMC ULTRAMAG .38 Special caliber, constructed entirely of a brass type material, and plastic pusher disc located at the base of the projectile. NOTE: PMC ULTRAMAG 38J late production made of copper with lead alloy projectile is not armor piercing.
bullet OMNISHOCK, a .38 Special cartridge with a lead bullet containing a mild steel core with a flattened head resembling a wad cutter. (NOTE: OMNISHOCK cartridges having a bullet with an aluminum core are not armor piercing.)
bullet 7.62x39mm with steel core. (NOTE: these projectiles have a steel core. Projectiles having a lead core with steel jacket or steel case are not armor piercing)
NOTE: THE FOLLOWING CARTRIDGES HAVE BEEN REMOVED FROM THE DEFINITION OF ARMOR PIERCING AMMUNITION:
bullet 5.56MM (.223) SS109 and M855 Ammunition, Identified by a green coating on the projectile tip.
bullet U.S. .30-06 M2 AP, Identified by a black coating on the projectile tip."
Also of note, the 5.7mm round has these designations (the SSxxx numbers are the names of the types of bullets)
SS190 — Armor piercing (AP)
SS191 — AP Tracer
SS192 — Hollow Point (not AP)
SB193 — AP Subsonic
SS195 — “Green” – lead free hollow point projectile with copper jacket (not AP)
SS196 — Sporting round (Hornady 40 gr. V-max, hollow point lead), (not AP)
There are other rounds out there for the 5.7mm but I'm not sure what their status is exactly, but FN Herstal (the company that makes the P90 and Five-seveN pistol) restricts sales of various loads to military and law enforcement only.
Again, State and local laws vary and can be more restrictive than Federal laws.
Now for the article Cali linked. I'm not seeing any details regarding the AP rounds, but if they're up for sale, they're likely rifle cartridges that are legal for ownership (M2 AP for .30-06 is the most common that I'm aware of and is noted for its accuracy out of an M1 Garand and M1903 Springfield, two popular surplus guns). Seeing that illegal sales are happening on the net is no surprise as it's not limited to guns at all (see Craig's List for their infamous "personal" classifieds among other things). It's also possible that some of those guys the author interacted with were ATF agents setting up stings. He also doesn't mention the majority of people who sell guns professionally or privately won't do shady deals because of the penalties involved (not to mention it's a good way to get yourself killed if you try to sell to the wrong guy and he just decides to kill you for the weapon).
All in all, that article is fairly poorly researched and more alarmist than informative.