An agent's "me" is its model of itself. This is already a fairly complicated thing for an agent to have, and it need not have one.

Why do you say that an agent can "directly perceive" its own mind? Or anything else? A perception is just a signal somewhere inside the agent: a voltage, a train of neural firings, or whatever. It can never be identical to the thing that caused it, the thing that it is a perception of. People can very easily have mistaken ideas of who they are.