Why shouldn't you get a ticket if you didn't have your drivers license with you? Why would that tick you off?? If you were in the same situation and had an accident, you would go to the pokey until someone figured it out (maybe after a day or two).
I don't think it has anything to do with being a tourist, or driving a rental car, it's all in knowing what's going on, and how to deal with it. I have driven rental cars many times in the past 3 years when I have popped over to Santo Domingo for a week or 10 days at a time, and never had a problem.
The police do conduct roadblocks to check for weapons periodically. Maybe you really don't know it or have heard only small hints before, but there is a weapons problem in the DR. They seem to go through the publicos and taxis completely, but not one officer has ever even opened my door to look. Normally, once they see I am a gringo, they usually just wave me on. Otherwise, I crack my window and they just ask me if I have any weapons, and I just tell them I don't need one, because I'm a gringo. That has worked to get a wave through the checkpoint.
Away from the city, especially going to the South, there are military checkpoints in many places. Many times, if they aren't busy, one of them will step out in the road with a carbine to make sure you stop for them. A hearty " buenas tardes commandante" will get a smile, and give them a chance to shake the gringo's hand before telling you to drive safe. It breaks up their boredom between guaguas and trucks passing through.