I can't speak for others but for me, what chafes me about it is the assumption of illegality. If they were checking everybody for everything, that's one story but to single an NFA weapon out over everything else smacks of "I don't think you can own that so I'm going to ask you about it."Why do we get so butt hurt over a stamp? It's a tax you paid. What is so bad about showing it?
Short answer is only the ATF. Long answer is anyone whose land or range you wish to use. I enjoy pulling out all my form 4's.