Uniform methods are an important aspect of a RESTful system, just as important as Uniform Resource Identifiers. The client of the system has to know what the methods are, so if you define your own methods you put a burden on clients to implement those methods in order to use your service. HTTP provides a set of methods that are sufficient for most RESTful services, and the methods in HTTP are widely implemented in existing libraries. Base your service on HTTP's methods and you've enabled a huge number of clients to use your service.

It's not so much that HTTP itself is RESTful. It's more that using HTTP's existing functionality instead of reinventing your own is RESTful. REST is a set of design principles for building software on top of HTTP.