No. That is incorrect. Even fully automatic long-guns (think AK47, AR-15 with a full-auto mod) can be owned legally after paying for the license with the ATF.
Paying for a $3k or so license, have the ATF, FBI and whatever other alphabet soup agencies turn your history inside out, and then buying one of hundred few, $10k+ fully automatic weapons.
It’s only half true. New transferable fully automatic weapons have been illegal since 1986.
The few that are out there are collectors items costing upwards of $20,000.
So while it’s tecnichally true that if you live in a state where they have not been banned outright you can legally buy a fully automatic assault rifle in the US, they are extremely rare and expensive.
People who buy them don't go on shooting sprees.