Beano- I don't think they FROWN on it, it's just that when we did Capt. Marvin's, we got all the way to the tender & realized we did not see any towels, not even on the gangway as DAP&I stated.
When we did the jeep safari thru Disney in Cozumel, the towels were sitting in the club we met at, and at Castway Cay there was a whole rack available just as you stepped off the boat.
You don't have to sneak like a thief in the night. I would just suggest going up to deck 9 & grabbing a few before you meet to tender into Grand Caymans, just to be safe.