NO! this is an OPPORTUNITY! if she takes her clothes off or something, he can use that way to check if she really has the birthmark. if all else fails he can just ask her if she has some kind of mark on her. she wouldn't know if its related to his birthmark.
I also kind of knew they're about to do it. it seems the timing and atmosphere going on in there was just for it. the fact shes being seen here as a maiden in love openly so when she's usually guarded around him...I also maybe think she got the stigma. SHE DOESNT EVEN HAVE HER GLASSES ON! something happened!