I agree, but I think we are talking about an essentially closed society, perhaps. Depending on his condition, they might just circle the wagons. I have seen it happen I am very sorry to say. LE is 50/50 I have found with letting it out. Some find a way to spill it to give the family closure-some just keep it tight depending on the MP. I do not know about Henderson, but I dealt with an awesome guy who was LVPD who did not let it leak at all...even though he spoke with the missing man on the phone. The family had to wait almost 3 more years before he surfaced.
...and I'll bet they were PO'd.
It's one thing to have the right to disappear, BUT your actions in public do not fall under privacy rights.
I think there'd be a way to notify a family that their missing loved one had appeared on a public street, without violating any rights of privacy.