So she didn't sleep with anyone else, owned up to it and presumably feels guilty about quite a minor thing. (Yes to all the self-righteous people on here, a drunken kiss at a moment where people do kiss each other IS a minor thing) I can understand her saying she couldn't remember at first because if she does feel guilty was probably thinking 'oh god, what do I say?! I don't want him to break up with me?!'
Don't focus on 'honouring your principles', that is like severing contact with a friend because they annoyed you once, fairly immature.
My advice, tell her you feel hurt but don't want to break up. If she is genuinely sorry about forgive her and move on, that is literally all you can do.
Above all else, don't go online asking for advice, actually talk to HER.