==Beth doesn't exist==
Kate just conjured up the name and person who supposedly likes Charlie'sDriveshaft to get friendly with him, so as to gain his trust.
-That theory is supported by the fact that Kate would not have much time to make friends, since she was on the run for much of her off-island life. I can't think of any times when she had the opportunity to befriend someone, with the exception of Cassidy and Kevin. Unless Kate met Beth while married to Kevin, it seems very likely that Kate made Beth up.