Sure they do - if they have probable cause otherwise. The last few times I went through these checkpoints (in Texas) they ran dogs around my truck looking for probable cause.
Whether or not you've crossed the border recently seems like fairly ineffective criteria. Are you sure that's the case? Where did you see that?
My experience: They had a drug dog sniffing at the vehicle without making it stop for the dog. They actually asked me to keep going, a little bit short of the stop sign, when I stopped for fear of running the dog over while it was very energetically sniffing in front of and at the sides of the vehicle.
Whether or not you've crossed the border recently seems like fairly ineffective criteria. Are you sure that's the case? Where did you see that?