I think Kate attempts to pass herself off as Claire so she can be rescued without being arrested. How she winds up with Aaron, we'd have to wait and see.
Off the wall theory...maybe Miles gets the $3.2 million from Ben and the *he* Kate tells Jack about is Miles. I'll bet Miles thought getting roughed up by Kate was "hot" and she obviously can't resist a man with money to screw over. Miles probably doesn't do "taco night" either.