I don't think the point is a direct equivalence between sexual assault and dodgy political stuff. So yeah, in that sense the "believe women" doesn't really follow.
But some folks sure are very quick to either entirely believe or dismiss, by default and without a shred of thinking, evidence etc, whatever he/she said stuff, depending on preconceptions, assumptions, and whether they like what is being said or not, or who said it. It's quite amusing.