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.
People who buy them don't go on shooting sprees.
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.