Evidence? The dictionary disagrees with you. Dictionaries are compiled from the ways that people actually use language in the real world. Also, the etymology of "prove" has nothing to do with indisputable facts:

Middle English: from Old French prover, from Latin probare ‘test, approve, demonstrate’, from probus ‘good’.

Edit: I feel I was being a bit forceful with my replies here. You airing your pet peeve triggered my pet peeve with linguistic prescriptivism. Sorry about that.