I'm assuming that the evidentiary standards are higher for conflicts between noble houses

I'm getting the sense there isn't an evidentiary standard at all, not in any case. Each side argues their case and presents whatever evidence they like, and then the Wizengamot votes whatever the hell they feel like, nonwithstanding evidence to the contrary. Remember what Draco told Potter back at the train station: the Malfoys can get out of any accusations before the Wizengamot, like a non-noble accusing Draco of rape, simply because they've got the votes. Or the case with clearing Hagrid of blame: Quirrel said it would go ahead "because Lucius would have no reason to oppose it" (my words).