One must assume that types are roles for this definition to be equivalent to yours.

That's exactly the assumption I made when I came up with roles.

Is there anything to support this assumption?

It's one of the two things I insisted on when we were working on Apocalypse 12. (The other is "They're not interfaces in the Java sense. They have to allow code reuse.")

Now Moose can do what Moose wants, but if Moose roles don't correspond directly to Moose types, one or the other is broken as per the formal model we designed.

How then can does check the type of the attribute if the attribute doesn't have a type?

That part I understand. You can squint and say "If it passes the type check, then it must also pass the role check", but I can understand why Moose's MOP wouldn't necessarily want to add a heuristic to guess about that.