That is correct you should be able to have any arm that the military has. Most cannot afford F16's or M1A1 Abrahms Tanks. During most of our history you could possess all kinds of weaponry, crime didn't really start getting out of hand until they banned full auto weapons in the 20's or 30's.
With all due respect, that is another MSM lie. Full auto weapons are not banned by the Federal Gubmint.
All you need is a Class 3 license from the ATF. Granted the paperwork is a b*tch and the 'fees' involved suck, but if you eventually do get your Class 3 license you can have a house full of full auto weapons (and real machine guns to boot). Naturally, this is all subject to local and state laws, but in 'most' (many) states they're legal to own. And in the late 1970's we could even own them here in IL, but alas that's no longer the case.
NOTE: I haven't checked my ATF book lately on all state laws so I don't know the exact number of 'most states' off hand.