This is blatantly false. Private transfer of fully automatic weapon is fully legal, provided you live in the right state and register it with the ATF (and pay a $200 tax stamp).

The prohibition target the manufacture of such weapon for civilian market past 1984. As such, there is naturally a very high demand for a very low offer, and prices are astronomical, IIRC about $20k for a pre-1984 M-16 receiver. If you have the money to buy a such receiver and your state law do not prohibit you from owning the weapon, go ahead, fill the ATF paperwork, wait 6 months, and enjoy your full-auto M-16. With more paperwork, you can even shot it as a full-auto suppressed SBR. 100% legal.