To answer a couple of questions in one go:
Yes, Club O provides towels, both beach and bath, to guests. Guests can bring back the beach towels to the main office to have them replaced as they get dirty or sandy. They are very nice towels, and I understand they had a habit of (ahem) disappearing (no doubt to be souvenirs), thus no doubt the policy of charging for them.
Club O guests also get chairs as part of the service, so no, none of the staff would have taken the towel.
Unfortunately it was probably a non-guest who swiped it ("Uhur, uhur, lookit this towel I stole for the nudie place! Uhur, uhur!"), and Lreserve's friend got stuck between a needed policy and sticky fingers. If she'd had the same neighbors who could attest to the fact that someone walking buy had taken the towel, I imagine the story would have been different.
I too have never heard of a towel vanishing in such a way, but I believe it is possible.
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