Not true! I was admitted then spent 5 days at Medica San Miguel with Dengue hemorrhagic fever. The hospital did not demand payment before I was admitted. I did get a bill I had to pay in full at discharge. I paid it, submitted my bill to my US insurance company and was reimbursed. Very grateful the hospital was there to help with my emergency!
I had a kidney stone for which I was treated in Cozumel. This was a different hospital (CMC/Costamed), but (apart from the actual kidney stone part) was a great experience. Various family members have been treated for all sorts of things at Medica San Miguel. We've always had great care and have never been billed until we were leaving. The bills have always been very low compared to US equivalents and have always been reimbursed by our relatively crappy US insurer without quibble.
I keep hearing stories about people being made to pay up front and maybe it's true. I suspect that at least some of the time they're freaking out and not understanding that they're being informed that the Mexican hospital can't accept insurance assignment from US insurers and that they'll be personally responsible for the bill of some estimated amount.