I use double straps on my backplate, and generally don't wet them, and have never had it loosen, although I cinch them down pretty tight.
If I were using rental gear in some odd situation, I would probably wet it just to be sure, especially if it was a single strap rec BC.
If I were using rental gear in some odd situation, I would probably wet it just to be sure, especially if it was a single strap rec BC.