The brace doesn't make it a pistol -- the lack of a shoulder stock makes it a pistol. The very first AR pistols didn't have "braces," they just had a round buffer tube hanging off the aft end. Then people started putting the equivalent of a tennis ball on the end of the buffer tube, and then along came the "braces."
That said -- the argument that the "brace" could be reclassified as a shoulder stock is, IMHO, completely valid. This is why it upsets me every time I see someone on YouTube bragging about firing their new AR "pistol" and showing themselves firing it with the "wrist brace" tucked into their shoulder.
The law defines a rifle as a firearm designed (or "intended," I'd have to look up the law to be sure) to be fired from the shoulder. The use of a "wrist brace" to fire from the shoulder occasionally is an exception that the BATFE has been allowing -- for now. But, at what point do you violate the law? If you build an AR "pistol" with one of those "braces" and you know full well when you begin the build that your intention is to use the "wrist brace" as a shoulder stock -- IMHO you will be violating the law when you complete the build and start using your nice new NFA short barrel rifle.
If enough people keep posting those videos, sooner or later the BATFE is going to want to put the genie back in the bottle.