Very nice post here, and I'm glad to see it still floating above water for us new people.
I was a cop and then a detective for several years. I worked with Game Wardens and on public/military/federal property (concurrent jurisdiction) with valuable historic grounds, ruins, monuments, etc... In my time I never saw anyone detect in my jurisdiction, but I wouldn't have done anything to them, personally, unless they put up a fight or argued with me. I would have run them off, as it's my job, but unless they were just tearing the place up I'd have viewed it as rather harmless and not worth my time. The best thing you can do is lower your head, agree with the cop, and leave. Basically what everyone else is saying.
However, I *did* work with a Game Warden who was totally out of control. A man turned himself in for shooting the wrong goose one day on accident. He brought the goose, explained the mistake, and said he wanted to do things the right way. This is a guy, mind you, who could have just left the goose dead, taken the goose with him, or any number of other things and walked away. Instead, she CITED him. I couldn't believe it. I actually disputed this with her proclaiming that honest, interity-driven people like that are hard to find and that her actions just completely condemned his good will over an honest mistake. He's now more apt to lie than be honest. Fortunately the legal team did not pursue this charge as a misdemeanor and the guy came away with a 3 month hunting suspension from the grounds and a small fine. I, and 99% of the other poeple I worked with, would never have let it get that far; and I"d say it's the same for detecting.
Park rangers, though, are another story entirely. Avoid them like the bubonic plague. They're like mall cops, always searching for a reason to feel relevant... (no sibling rivalry there at all
Great posts, keep it up!