Rebecca is now an Unreliable Narrator
You could say that they had to retcon in the relationship with her college professor in order to give Josh a reason to bail. But, I actually really like what this does to Rebecca's character. She is so delusional, that we can't even trust that what she tells herself is the truth. And, it totally fits her character that she would completely black out her past experiences that were painful to the point they caused serious mental trauma.
Is there anything else that we the audience have taken at Rebecca's word that could easily be false? Rebecca did hint that she did some amount of stalking of Josh after he broke up with her at summer camp. It would certainly be interesting if we discovered that the entire pilot, or show for that matter, was just Rebecca's delusional, romanticized version of events. (hence all these musical numbers)