You are missing the idea that every single piece of evidence wasn't neccisarily meant to be literal. It might just be the writers way of symbolically starting the green hat trend. The key word is might, though, since we are not the writers and do not know for sure what the purpose of Ezlo giving Link the green hat was. I am just saying not to claim that you know it wasn't supposed to mean anything since you were not a writer for TMC, either.