Basically, nothing is illegal for a civilian to have per the 2nd Amendment, there's just some hoops to jump through depending on which state you live in and what you're buying. WoodenPlank, Rockpup, and quite a few other members here have things that most would think are illegal, but it's largely just arbitrary. For instance, WoodenPlank has a rifle that's like 2" shorter than the law allows, so he has a special piece of paper that says he's allowed to own it.
But, FYI, there's nothing illegal about a .50 BMG rifle. The only thing "illegal" about that gun is that it's fully automatic.
There's no permits or paperwork needed to borrow or rent, though. So if he knows someone who owns the gear, they can let him shoot all he wants. For the money DoughBoy just mentioned he could be renting from someone.