They've said that every year for the last 10 or more. I've hunted in NM going on 20 years and only been checked twice and both times was a positive outcome. They were professional and courteous. In fact, the times I was checked it wasn't even a road block. One came into camp to check a deer we had hanging and another time I met one on a trail. I just pulled over and handed him my license. After small talk, he directed me to where he had seen a buck about 30 min earlier and was able to get him. We've been checked more times by Forest Rangers than by Game wardens.
Same here, but what I have seen is a high number of poachers and particularly during muzzle load season! In 2001 in Unit 15, a muzzle loader unit, we had set up near a water hole on an elk hunt and heard a nearby shot. So we packed up to the truck only to see a man and his son coming down the road with a "spike" bull in the back. While talking with them I noticed bolt action rifle
in the back seat that was not a muzzle loader. In '05, I came upon a group that was field dressing two cows during the BULL ONLY season.
I fully support field check stations. Many national forest utilize field check stations, such as the Sam Houston National Forest, where there's an ample supply of "wing nuts" driving around!