Eternal Sunshine of the Spotless Mind chronology question.?

Alright. So i get that the movie is extremely out of order, and ive managed to get my head around the order of most of the events of the movie :meet at beach party, relationship, brake-up, clem gets her mind erased, joel gets his mind erased, meet a second time after joel runs away from work (beginning of the movie), he brings her home where the tape is discovered (end of the movie). The only problem i am having is this: When they first meet at the beach party, Joel pokes fun at clem by singing the "Oh my darling clementine..." song. Later along the timeline the two are talking on the train as new acquaintances. Clem tells Joel not to make fun of her name and specifically references the same song. Joel, however, says that he has never heard this song. Could it be that his knowledge of this song was erased with the rest of his memories? It almost seems that on the train Clem remembered Joel and the say that they had at the beach and is attempting to jog his memory in hopes that he remembers her as well. Also, when they first meet at the beach party, Joel says that she was quite comfortable around him, as if they were already lovers. It seems that all these events suggest that they knew one another even before the beach party. Does anybody have an explanation?