You've repeated this take twice, but it is still wrong. Yes, the fastest water molecules on your skin escape. But you also have water from the air also latching onto your skin which you aren't accounting for. You're free to see how well evaporative cooling works when there is a lot of water in the air. You can just take a fan into a bathroom and run the hottest shower possible for a few minutes.
I think this phenomenon does not take in account the wind. That actually if you have water to wet yourself and a fan you can cool you down.
Not sure though since I seem to be alone to think so.