Currency/money in other countries.

We have used U.S. cash for almost everything we've purchased in the islands. We have occasionally prebooked excursions independent of the cruise line with vendors where we have had to pay beforehand with a credit card. With credit card skimmers all over, I wouldn't trust using my card in the Caribbean unless with a very reputable merchant.

In our experience it is not a myth. We have had bills inspected very carefully and have had someone ask for a newer bill, mostly in the Caribbean but also in South America.

Does it always happen, or even often? No, but maybe a half dozen times in our experience, and they weren't beat up, torn, dirty bills either, just not crisp and new. It seems to happen more with excursion vendors or with larger bills.

Perhaps they are hard to exchange for local currency if not in very good condition.

Certainly all the countries OP was talking about, as well as a number of others. I have never had a problem having reasonably used or wrinkled US bills accepted - so the notion of ironing them is silly. Of course if you are talking about torn or really filthy bills, I can see anyone, anywhere - even in the US being reluctant to accept them; but seriously - how many of you carry torn or really filthy bills in your wallet?

Again, how many countries have you traveled to?

Bills that are readily usable in the US may not be accepted in some countries.

Yes, even just wrinkled.

Take such bills at your own risk. Yes, you may be fine. But you may find yourself with cash that you cannot spend. At least you will save money. :D