Got some dealings with faculty (at a large state Univ) regarding IT security policies myself. Like someone once said, you can talk to faculty, you just can't tell them much. Still got one option Im keeping in reserve.
To OP, I would hope you organization has a policy that says when and under what conditions you are able to view logs to confirm normal system operation (which effectively was called into question). Provide him a link to that and that should just about put it to bed.
And BCC the prof on the reply.