And yes, he's basically just memorizing everything. We're still working on the "reading music/recognizing notes" thing. :-) I think the idea of just learning some songs while just introducing music-reading (as opposed to a huge focus on the latter at the beginning before learning any songs) is supposed to keep the learner more motivated and excited in the early days.
Oh, and P.S. The second song, he really JUST started it. He had been assigned it the week before, and then the sun came out and he spent every day playing outside not coming home until practically bedtime. Somehow he got the right hand pretty much down after the equivalent of one and a half practices.