It resolves, causing the triggered ability to go on the stack which would bring Griselbrand back to play. In response, I Disenchant Animate Dead.
My friend believes it would be the same as the bouncing Oblivion Ring trick-- the triggered ability would still activate, causing Griselbrand to come out, but the aura would be gone before its "leaving the battlefield" trigger has anything to target: i.e. Griselbrand comes out and stays out, while Animate Dead goes to the graveyard.
This sounds right. Is it?