I've worn rolex, omega and iwc in Mexico and have never been "arrested" by the police...
I'm not saying there are no crooks anywhere but there are about the same amount in Barcelona, Madrid, NYC, LA, Detroit and Washington and Moscow.
...anyway.
If you're afraid or you're in an area where YOU don't feel safe, sure, hide it. Of you want to wear it wear it.
As per your the OP question, nothing to worry about an AT on the beach, as long as you accept the wear. If you hate desk diving marks on your watch you will have even more actual diving marks.
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