The problem with your question, is in the way it's worded. For starters, it assumes that permission is needed, to begin with. I believe that unless detecting is specifically (by name) dis-allowed, then "permission" is not needed, to begin with. For example, would you have "asked permission" to fly a frisbee? Drink from the fountain? Stand on your head there? etc.... If it is not specifically dis-allowed, then I consider it "implied permission" until told otherwise.
And no, I do not consider defacement, or disturbance of vegetation, or any other such clauses to apply to us. Because if
YOU know you'll leave no trace of your presence, then why would those clauses apply to you? To think otherwise, is to already have lost the battle. Because those clauses exist everywhere, on all public land. I mean, think of it: if you walk into
ANY park (even parks where it's always been considered open-game), and ask some desk-bound clerk "Hi. Can I dig and destroy the park please?" What do you think the answer will be?
I have seen time and again where there's been parks where no one's ever had a problem (yup, in full view of gardeners, passing police, etc....) It's just ignored, and no one thinks anything of it (unless you're being some sort of nuisance, or leaving a mess, or something). Then PRESTO: someone goes to city hall and "asks permission". They get a "no". Why is that? Because the mere fact that you felt you needed to ask, simply pre-assumes or infers that you are somehow doing something that will be illegal, or damage something etc... (lest ......... why would you have asked, if it didn't need permission, and didn't cause any damage?). Do you see how the question itself simply dictates the answer? And then presto: they'll find something to morph to your "pressing question"
Unfortunately we're in a hobby that's sort of like nose-picking: No one really cares if you just do it discreetly. But if you start asking people "can I pick my nose?" they're going to tell you "no".
I never ask permission at any public park I go to, and rarely ever have a problem. Obviously go at low traffic times, be discreet, don't do obvious historical monuments, etc...... As an old saying goes: "sometimes no one cares .......
UNTIL you ask"