"Un-authorized power" ? I too used to think there had to be a specific rule (eg.: saying "no metal detecting" etc...) for them to boot you/us.
One time I was detecting a park, in a city not far from me. It was a park that had been detected routinely (since the 1970s as a matter of fact). And I know for a fact there is not city or park rules saying anything about detectors. However, this one time, a city employee came and booted me. Just said vague things like "you can do that here" etc..... I should point out that I was not retrieving any target at the time (was just waltzing about swinging/walking). So "holes" was not the issue. Nor was there any evidence that I had been anywhere there (ie.: you could not even tell I had been there).
At first, I tried to challenge the guy. But after he started to get a little .... uh ... terse, I just packed it up (as I was getting ready to call it a day anyways). Once I got home, I did some researching, and confirmed that I was right: there IS NOT laws or rules about detecting in this city. So in my mind's eye, this fellow was using "un-authorized power" (as you say). And I talked to a lawyer friend of mine, telling him about this encounter.
HOWEVER, the lawyer friend told me some interesting legal info that applies to our situations here: As much as you and I would like to THINK there needs to be a "specific law", this is not the case. As arbitrary and capricious as it may sound, there does not need to be a rule or law saying "no metal detectors", yet a cop or city person can still do that. I objected to my lawyer friend and said "no way!". But he explained: Laws are purposefully written vaguely, so as to apply to a myriad of situations that may arise in the field. In other words, there's simply no way EVERY SINGLE situation can be predicted and laws-made-to-address. Because otherwise, everyone would be endlessly debating semantics with officials. You know, like if you walk around with only a single sock on, you could debate the cop and say "but officer, I was not technically nude, since I had one sock on", and so forth. Therefore there vague and nebulous laws that do things like "forbid annoyances".
Yes, this does seem arbitrary and capricous. But there's just no way the law can predict every single future potential. Therefore cops and "duly appointed city personell" are given latitude of interpretation to do their jobs. And their superiors (or judges, etc...) will usually side on the side of the "duly appointed official" (unless it's a truly agregious abuse of power). Because if they perpetually sided on the side of the other person, then cops job morale would plumitt. No one would ever want to be a cop. Everyone would be arguing with cops, debating semantics, etc... Therefore most of the time, you're going to be on the loosing end of ability to fight such a thing (unless truly agregious abuse by a cop).
And let's face it fellows: Our hobby DOES have admitted "connotations" to some people (that you might make a mess or leave holes, or "steal cultural heritage" blah blah). And while it may be true that YOU will leave no trace or that YOU were only poking 1" for surface clad, yet ...... in their mind's eyes, they just don't want to be bothered.
So to be honest with you, it's just gotten to where I hunt parks and turf at night nowadays. So peace-ful. So serene. If I were to get booted by a cop (as you seem to say happened to you there), I would just make note of what shift that was on, and simply a) wait a few months, and b) next time I go, go at a different shift time. Like if that was 8am, then it's safe to say that he's not working at 6pm, and so forth (as he's evidentally on AM shift).
OH, and one more note: The fact that this "power" rests with authorities to interpret-as-conditions merit, does NOT mean that the way to avoid such things, is to go ask ahead of time: "Can I metal detect?" Because if you do that, then you merely risk someone saying "no", when 1) no such rule exists, and 2) they might never have cared nor given the matter a moment's thought. In other words: there's been places where no one's bothered, yet someone finds themselves a desk-bound bureaucrat to tell them "no" anyhow.