Suppose you like someone very much. Then, by a familiar halo effect, you will also be prone to believe many good things about that person - you will be biased in their favor. Most of us like ourselves very much, and that suffices to explain self-assessments that are biased in a particular direction.
The experiencing self lives in the moment; it is the one that answers the question, 'Does it hurt?' or 'What were you thinking about just now?' The remembering self is the one that answers questions about the overall evaluation of episodes or periods of one's life, such as a stay in the hospital or the years since one left college.