Perhaps one aspect of my logic wasn't clear: I assume that these FAMs -- or any other LEOs, for that matter -- would conclude that arresting somebody for handing out tootsie pops is unreasonable and would let him go. I once had a police officer question me about shoplifting in a mall parking lot, while I was walking toward my parked car. Obviously they were looking for somebody else, as I have not shoplifted in over 40 years (I got caught, incidentally!). I did my usual, "Am I under arrest" routine until he got tired and let me go. He obviously concluded on the basis of this legal back-and-forth that I was not the shoplifter he was looking for.
Similarly, the FAMs in this case would likely have concluded pretty quickly that they were not dealing with a terrorist and sent him on his way. Under these circunmstances, the probability of sitting in jail while an investigation takes place is close to zero -- although not exactly zero, I must agree.
Bruce