There are a couple more things that you should think about with this scenario. They would be the energy or attitude of the prople involved. I am sure these park ranger guys projected an attitude of authority, it has been my experience that most people in uniforms connected to some kind of law enforcement tend to be jerks. They do not always treat people very nice and I am sure your dog could sense how these people are. Secondly you were probably projecting nervous energy that your dog picked up on. You said you were glad you did not get a ticket, this leads me to believe that at least at some point when they first approached you that you were nervous to some extent. Law enforcement people can be very intimidating and I know that I do get nervous when approached by them. You can do all the cute little excercises with strangers and treats that you like, but in the end they will not help if you are not calm and collected. Hopefully I have been clear enough that you get what I am trying to say, it is clear in my mind what most likely caused this versus if you had just happened along a couple of other hikers on the trail and the dog would not have bitten if you had shaken one of their hands.