There are no kissing "accidents." I've never accidentally kissed a girl in my life.
She consciously decided to do what she did without regard for you, then when her guilt ate at her, she told you not because you deserved to know, but because it would make HER feel better.
It's pathetic to keep her around after that disrespect. You shouldn't be in a LDR anyway.
When I was 20, I was screwing a girl who had a boyfriend at another college. She decided she felt guilty about it. She told the boyfriend. They didn't break up. She went right back to screwing me soon after. All she cared about temporarily was her own conscious.
If anything, i'd say to keep her around and use her to keep fvcking until she caught on you weren't really in a relationship anymore, but since it's long distance i'd say just walk away and to hell with it.
. Sadly it seems not.