I believe that the thread's original question (hats = skills?) has been proven to be nothing more than a popular misconception. I have to admit that some of the posts here are really quite good, though. I can totally agree that in many of the scenarios you encounter in TF2, you can estimate roughly what skill level a player is around. But that only gets you so far, taking into account that a lot of great players, especially professionals, stick to minimal cosmetics and barely any flashy items or skins. However, I like DingdongJR's post a lot. Usually one would assume that because a player's got good items, they have the money to waste on them. Doesn't have to be any more than that. But I strongly believe in effort and dedication, so I feel this point of his is especially true. Acquiring items should be done if you have the intention to actually keep on playing and put in effort into the game.
I'll say that I usually play without any cosmetics. People usually find that threatening, and when you run into players you can beat it's nice to have them think twice about someone's skill level just because they look like a new player. A "free-to-play" may not play like a FtP at all.