Yes, this is often the case at private hospitals in Mexico. "Mexican facilities often require payment 'up front' prior to performing a procedure, and most hospitals in Mexico do not accept U.S. health insurance," stated the US State Department.
"I can tell you horror stories, but it's better to be brutally frank, indeed. You better make sure that your insurance company will cover you for immediate entry into the hospitals of your choice in your vicinity, without first having to come up with a cash deposit. When and if having a coronary or stroke, this can be devastating. Contact the hospital administrators of several places and even verify that they will honor your insurance company's commitment, indeed. Get them even to sign something and carry it around in your wallet. I wouldn't trust social security hospitals and I have many Mexican friends that wouldn't, as well," remarked one expat.