pulling together a few important points from a few brilliant ws-ers, plus a few of my own
IMO...
1. People keep mentioning the "change" in KC; she was quieter / more reserved / a better person back then. I don't think KC's personality suddenly changed. She's always been a chameleon. I think what changed was that, sometime a long the way, she stopped playing the role of good daugher / studious high schooler, etc. She probably used to work very hard to appease CA, keep up appearences, etc., to obtain the privileges of a "good" daughter. She couldn't even admit to CA that she was pregnant, because it would shatter that facade.
2. For whatever reason, admitting who Caylee's father was would further damage that image. One night stand she can't remember? Too many guys in a short time frame? (less likely in my opinion, but a possibility). An older, married man? That Latino guy she always thought was hot? (sorry, not meaning to be offensive, but we have heard that CA could be innapropriately judgmental in that way). Either way, it presented a better image to latch on to Jesse - "look mom, we're being responsible grown-ups, getting married, etc"- until Jesse actually had the nerve to count backwards, get a DNA test, and put an end to that whole scenario.
2. At that point, KC is still trying to maintain the good daughter image (CA is, after all, her "best friend), and any of the above scenarios would not go over well. In comes this straight-out-of-a-soap-opera car accident story. Not believable in the least, but...
3. ...the perfect scenario for CA! KC is still a good daughter - a victim, actually - and the BEST part is... CA doesn't have to share her precious Caylee with anyone! She hated those pesky Grund's being involved with HER darling grandaughter. She'd much rather go with this mystery father theory than have to share with anyone else - even if it meant giving up those support checks a long the way (which, IMO, if existed would go straight to CA, with KC receiving an allowance where CA saw fit). CA's happy she gets Caylee, KC is happy she doesn't have to admit any further transgressions, and that's that.