There may (or may not) be additional factors involved. For example, it is possible the FBI may fail to complete the required background check within a specified period of time, and the application may enter some status that is neither "approved" nor "denied". In addition, many AR pistols equipped with braces already have standard (short non-adjustable) pistol buffer tubes/receiver extensions. Finally, I have seen it stated repeatedly that the ATF's position is "once a rifle, always a rifle". Whether that is true or not, or true in some cases and not others, I do not know (I am not a lawyer), but it seems that the point in time at which ATF considers or considered any specific brace-equipped pistol to be an SBR may influence the ability to convert that specific firearm to a legal non-braced pistol, rather than to a legal non-SBR rifle (with a barrel 16" or longer).
I am not trying to pick a fight - just suggesting that when it comes to federal firearms laws and regulations, things are sometimes not as simple as they appear.
;^)
Technically, that should read "starts a rifle, always a rifle." The ATF has repeatedly said that a pistol could be converted to a rifle, then back to a pistol again without penalty, but a rifle cannot be made into a pistol.
And it all goes back to the original 4473 that the firearm or stripped lower was first transferred from an FFL to the first owner. If the 4473 says "pistol" or "other," it can be a pistol or a rifle interchangeably. If it says "rifle," even if the item was a stripped lower, it can only be a rifle.