The act prevented any new fully automatic weapons from being bought and sold in civilian hands if the weapon was first registered after 1986. If the weapon was first registered before 1986, it can still be legally bought, sold and possessed under federal law both now and in the future. (Of course, not all states allow these weapons, but that's another matter.)
I do believe you're both wrong, and that it was Bush the Elder's administration that signed-up for this ban in '89 or '90, just one more of his campaign promises that he famously broke.
Shortly before his famous "Read my lips..." statement on taxes, he made a clear and unequivocal statement that there were quite enough gun laws, thank you, and that he would permit no more restrictions upon our right to keep and bear arms.
I do believe this particular act of perfidy caused many a gun owner to sit out the '92 presidential elections or to vote instead for the "hand-grenade with ears."
So no, I have little use for the Bush family pere et fils.