I would not worry one bit about entering into Mexico or any Latin America country with a DUI on your record. In fact I wouldn't worry even if I had a felony drug record but I might expect to get searched! Now if you had done time in prison for say rape, arm'ed robbery, ect, you may get hassled or refused at the border. And rightly so IMHO....
As the police officer said above, just play your cards right, if it does come up deal with it accordingly. And what he says pretty much rings true even with corrupt cops trying to rob you. They have no way of pulling up any info on you out on the road but I still wouldn't lie to them or push the limits in a situation.
And FYI, I have been across the Mexican border 4x in my own vehicle but I have no criminal record.