A lot of brace manufacturers flat out lied when they claimed that their braces were approved by the ATF. I started looking into this several years ago. Here is what I found along with the sources so you can look them up and verify that the same stuff I saw. Years ago I learned to go back to the source documents and read them for myself rather than depending on someone else's interpretation.They didn't "overlook" it. They told people braces were legal. Millions of people bought aftermarket and OEM braces. This is a common use item now.
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From what I have seen, they all depend on three letters sent to SB Tactical (from 2012, 2015, and 2017) and the ATF's 2015 "Open Letter on the Redesign of "Stabilizing Braces"" and a clarifying letter on March 22 2017. You can get the SB Tactical letters from their web site. In the 2012 letter, they described the brace sent and its use. The letter stated "...we find the device is not designed or intended to fire a weapon from the shoulder".
The December 2015 Letter to SB Tactical includes photos and includes the statement "Central to ATF's determination is your representation that the purpose and intent of your design, as with previously approved designs, is solely to allow shooters - particularly those with disabilities--to better support large handguns or pistols when firing one-handed." They even insist that the rear of the brace have no ridges, "a feature commonly associated with butt stocks/shoulder stocks" in order "as to preclude its usefulness to be shouldered". The 2015 "Open Letter" states "The pistol stabilizing brace was neither “designed” nor approved to be used as a shoulder stock ..."
In the March 22 2017 letter to SB Tactical, they pointed out that the submitted and approved sample "... cannot be comfortably fired from the shoulder".
The 2015 "Open Letter" states "Any person who intends to use a handgun stabilizing brace as a shoulder stock on a pistol (having a rifled barrel under 16 inches in length or a smooth bore firearm with a barrel under 18 inches in length) must first file an ATF Form 1 and pay the applicable tax because the resulting firearm will be subject to all provisions of the NFA. "