Married women, will you answer?

I saw my girlfriend talking on facebook with a childhood friend who's also an ex boyfriend of hers. This conversation occur ed over the course of about a week. He said "I really like the pic of you and your mom". She said "tyvm I'll tell my mom u think shes hot! jk how have u been?", he said in response "Your mom is hot. Im fine. Just workin and havin a good time. How you been?" Then she said "doing ok just working a lot. nothing new going on...so since my mom is hot and i look like her that makes me hot righ!? *jk* hows ur grandma doing since her accident?" then he said "Of course your hot. Last i heard she was doin good. She should be back home now or gettin out soon." and finally she said " awesome! good to hear from you. ttyl" Now I know nothing of their relationship except that they grew up together, they dated and were ually involved, he broke her heart, and he likes to joke around a lot. I think this conversation was in appropriate considering we're in an exclusive relationship so I told her how I felt. I said "I don't want to overreact but I just want to let you know I saw the facebook messages you and Bill (names have been changed to protect privacy) have been exchanging and I thought that it was inappropriate that he's calling you hot." She said, "I felt comfortable saything that to him because I know in my heart that I have no feelings for him." I wanted to believe her so I told her "I want to believe you but I'm having a hard time understanding because if I was in the same position with an ex girlfriend I would only be telling her she's hot to be flirting with her, how would you feel if the situation was reversed?" She said "I'm not a jealous person, if you want to find someone else let me know, it's whatever you want." I don't feel that way for her. I can't say that to her and be ok with it. I don't want to loose her. If it's really what she wants I reluctantly step aside but I'd be crushed. Am I crossing a line by being apprehensive about this situation? Should I adopt a "whatever makes you happy" attitude?