Some people have argued that Fedora is not a hat, it's a project. But if our project's name is the name of a hat, why not using it to represent it?
Quite simply, it's mostly because of trademark law. Wearing a blue Fedora dilutes the Red Hat trademark, and we don't want to do that to the primary sponsor of our project. Trademark law is clear on the requirement to keep your registered mark from being confused with other marks.