Quesion about the movie "Black Swan"?

i saw it last night for the first time and i think i understand most of it. The only thing im not completely sure of is lily. i think we can all agree she wasnt really out to get nina and that lily herself was indeed real (many other characters notice her presence). However, did nina and lily really have sex or was it all in ninas head? (most ppl say no) Lily admitted to going to the club and doing ecstacy with nina but she denied going home with her (she claimes she went home with a guy from the club). I kind of could see how she might of imagined it since ninas mom never says anything about lily when nina comes home iwith her. HOWEVER, i think one thing gives it away. When nina went to her room with lily, she locked the door with that wooden stick. BUT when she wakes up, the wooden stick is no longer in place (its no longer blocking the door and and nina notices its moved) so this must prove that lily was there. she must of moved it when she left in the morning. why else would nina move it herself? what do you guys think??