What I have wondered is, was this done as a bribe for the woman to get out of some sort of trouble? I have not followed this closely, but it seems likely. And even in NM I bet this is illegal...
I think it was a “romantic tryst” of sorts with consenting adults. I wish I was tech-savvy enough to find the original posting on the topic. The FR comments were hysterical (rated R but funny). For whatever strange reason, there is a small dog that looks exactly like a meerkat in the photo.
I think his firing was probably caused by him being on duty at the time. Yes, he was in his police officer uniform (although the Sam Brown is swung to one side) and it does appear to be on the hood of a police car. We live in crazy times!