As Kate was a 'veteran' from previous shows, I see no reason not to use her. "Neccesity knows no law".
No reason to lie about it. She HAD been in the show before, so rehearsal not as desperate in her case. Simply say-if anyone asks, the others dumped on you at the last minute and you had no other immediate options. (Plus I wouldn't cast the other three again, they're obviously unreliable!).