Liberals can't even get their lies straight. The NFA did NOT make machine guns illegal. In those days, the gun grabbers wouldn't dare ban any kind of gun. Instead, they used the Interstate Commerce Clause to regulate, but not ban, the weapons. They figured this loophole would allow them to place a prohibitive tax on each transfer of a machine gun, allowing them to virtually ban the guns, while claiming to merely apply "reasonable restrictions".
In those days, they knew they could not outright ban any kind of gun. The thought process of the gun grabbers has now degenerated to the point where they think the federal government is the sole source of permission as to who can own what guns. To them, the debate is already over, and it's just a matter of time until the government demands we turn in what little it permitted us to still posess.
You are correct. It is not illegal to own full-automatic firearms. I know some people who do so. It requires a Class III firearm license. The thing is that when Clinton took office they quit issuing them. They only allowed those who had them to renew them, and pressured those that had them to not get them renewed.
I don't know what the issuing status is in the Bush administration, but it is still legal in some states to purchase and own them if you can obtain the proper license.