She's trying to get you to become more emotionally attached to her. Obviosuly, you should not play along because you are gonna get burned if you develop more of an emotional connection to her.
But she's gonna keep playing this game, she'll keep bringing it up and everytime you refuse to play along, she will withdraw from you. So everytime she pulls back, you'll invest a liiiiiiiiiittle more in her, just enough to make her "happy" again but not enough to get yourself in trouble. But 20 times 'a liiiiiiitle' equals to A LOT........ She sinks her hooks into slowly, man...without you realizing it, you are getting more emotionally attached to her...
So stay firm and resolute. Don't play along, just don't. Like you said yourself, she accepts you like you are or she moves on from you. Be prepared for her to move along, accept that this might happen and that you'll be ALONE then. Don't let the thought of being alone make you compromise yourself!
It is not better to be alone than to be with her... Unless being with her requires you to play along with her game!! In that case it is definitely better to be alone! Get it?