I'd argue that skipping should earn you the hat. If you're skipping, you're not robo-reviewing - it means that you're deciding that you aren't qualified to judge this post. We should be encouraging people to skip more. People too often will review something even if they're not qualified to. Skipping is a fundamental part of review.
This hat already kinda encourages robo-reviewing to get the hat. If skips are included, that does much less harm than have people blindly robo-review actual stuff. And no, audits don't do much good, given that they're only on a few sites. Robo-skipping does much less actual harm than robo-reviewing actual posts.
What seems best to me is including a certain minimum number of actual reviews, and letting skips fill in the rest. So I could make ten reviews, and skip ten items, and get the hat for reviewing responsibly.
Don't encourage people to make reviews on stuff they'd skip for a hat.