The book you gave me...

I think that most people agree that the Ending was disappointing.
But also, did I miss something or did they even make a mistake in how they found out which person was which in the end?

Tobi said before that the book that Spencer had was highlighted and written in, and that the book he recived when he was kissed Goodbye by "Spencer" was not (and we knew it was Alex).
But then to test which person is Alex and which is Spencer he askes "Which is your favorite poem in the book that YOU GAVE ME". And Spencer starts to recite it... but how would she know which book was meant as SHE never gave it to him?

Did they mess that up too or did I miss something?