Montazuma's Revenge is very real. There is a parasite in the water most areas are too poor to properly filter out. The locals are adapted to it, so it has little effect on them, but visitors will get extreme diarrhea.
No, in the city I'm not sure but the small towns like where my family lives no one drinks the water there, everyone there gets a weekly delivery of drinking water.
In tourist resort areas, they have updated filtration systems so that the water is drinkable. Outside of those areas, you should stick with bottled water or other bottled drinks.