At 5:54, Casey Kasem briefly talks about Karen's audition with Kenny Roger.....
That might explain the "why", but then it just might be Kenny's weak, flimsy attempt to cover his ass a little later because he blew a big chance to have the best female singer in pop music history in his band...This presumably puts to rest the "why" as to Karen not being selected by Kenny and his band. He simply didn't think she was the right sound.
I'd also note that since Kenny (according to Kasey K) said that she had a very sweet voice, this should put to rest any notion that Karen did anything other than try her best to win. Something I personally felt certain of, in any event.