Each situation has played out differently based upon how far away from the tourist zones I've been and how rural the location was. My most-terrifying experiences have been in Tulum and Colima.

My suggestion is that anyone going to Mexico should be prepared with cash-on-hand to provide a bribe in dollars, not pesos. I always have a $20 and a $50 that I'm prepared to part with as part of the cost of being in Mexico. I try to keep them in separate pockets so I can try with the $20 for minor problems and the $50 for more serious ones.