Popular misconception. There is no federal prohibition upon private citizens owning full auto weapons.

The NFA of 1934 was the first federal gun law (save for a ban on sending handguns though US Mail). It made ownership of full auto weapons subject to a $200 tax (at the time, several times the cost of a typical such weapon), fingerprints on file, and sign-off by local law enforcement officer. The federal picture on ownership of full auto weapons is statutorily pretty similar today. Of course many peripheral laws have been passed that make such ownership less and less practical.

What states do is somewhat different. I assume Nevada allows such, but I really have no reason to look it up. I think they are legal in the majority of states.

edit: Ever wonder why federal gun laws are enforced by a division of the US Treasury? Picture 1934. Prohibition has been just been repealed. Depression is in full swing. What to do with legions of jackboots on the federal payrolls who have just had their reason for being on the payroll repealed? Obviously politically unpalatable to just lay them off (I guess the term at the time would have unapologetically been 'fired'). Why not create an entirely new reason for these revenuers to be on the payroll? Hence, the Bureau of Alcohol, Tobacco, and Firearms. Who cares if a few fringe gun owners get hurt in the process? It serves the greater good, donchaknow.