Stuart Varney had a Seal on this morning who stated that. And he said you’ll be regularly inspected. So, that means that fully automatic weapons are already virtually illegal.
Now there's an authoritative source.
Here are the facts: As long as there are no restrictions at the local/state level, a la NY/CA, an individual can apply for a Class III license through the BATFE. It requires payment of a tax stamp ($200 IIRC), an application that includes approval by your local LE chief, and a background check with photos & fingerprints. Upon approval, you can then acquire said firearm, assuming you have the deep pockets necessary. A recent quote I heard said $15K is about the minimum price for admission to that exclusive club. About the only thing that you think you heard that was correct was about being subject to regular inspection.
For your reading pleasure: