Incorrect. Any lower transferred as “other” can be built into either a pistol or a rifle. Doesn’t matter if a stock has been put on it. For it to be stuck on “rifle” it has to have been stocked AND barreled.
No idea on the date of the letter I posted, as I can't find the first page that goes with it.
Here's a 2010 letter which mentions "barreled" only, not "stocked and/or barreled" and would seem to supplant the 2004 letter...
IIRC, there's another letter floating around, and I can't find it at the moment, stating that a completed lower (even with stock) may be built into a pistol since it's never been barreled as a rifle.
If you don't want to use a heavy barreled upper, I suppose this is an option. But since you can have pretty much any barrel length at that point, I'm not sure why you'd go with 16".