You can , if you're a Mexican. If there's a hospital close enough to go to of course. Be prepared to wait. Pretty much like Canada and England, but even lower quality care.
Good or at least fair, care is available in Mexico, at least in some areas, but it's all private, in that way the system is not like Hillary's national health care, where you could be fined or go to jail for going to a private doctor or facility.
I’ve read that American tourists are held hostage until they pay their bills.