No, Zero, Teriyaki's correct with his numbers there.
I've twice now, for kicks, attempted to craft a random hat, curious to see just how badly Valve did on this part of the update.
Crafting Session 1
1st combo: 3 refined metals.
Result: Pyro's Brigade Helmet (which I already had)
2nd combo: 2 Pyro helmets.
Result: Heavy's Toque
Crafting Session 2
1st ccombo: Scout's helmet and Sniper's belt.
Result: Heavy's Toque (which I already had)
2nd combo: 2 Heavy's Toques
Result: Spy's Billycock
There was another one in there somewhere where I combined the soldier's stash and the heavy's football helmet, I think, to make something and got yet another duplicate, cuz i dont have those ones anymore. hehe
So, don't rely on crafting to get you what you want any time sooner than a random drop.
I'm still hoping that we can one day trade items with other people. I wanted to have a mini-event, so to speak, where I would give away hats to people that dominated me or whatever.