Ok Folks--there is one solution to this and it is quite simple!
We encounter the problem frequently in all-inclusive hotels in Mexico and many Carib islands
Hang on to your hats--are you ready--it's a real stunner:

move their towels elsewhere and play stupid:
"were you sitting here?--no one was here when we arrived!"
It's the truth, plain and simple.
If you get some lip about "we were at breakfast or wherever"
--sorry, we didn't see any "belongings".