Where do people get the idea that it's illegal to own an "assault rifle" or a fully-automatic firearm?

As far as I knew, an 'assault rifle' is just a rifle with a selector switch on it. And as for assault rifles and full autos, I thought as long as there was no law prohibiting them in your state, you simply had to do the run-around to get one. Buy the $200 ATF tax stamp, do the registration paperwork, get the FBI background check, and local law enforcement had to sign the paperwork and it's basically at their discretion to do so.