Don't ask if you don't need to.

It's always best to ask in person. Yeah, they would like to keep out people using a garden spade, and those who don't fill holes, leaving the sharp trash laying exposed. There are a lot more, non-detecting people using the parks, and they can't be expected to keep a safe environment, without keeping an eye on those digging holes... If you go to the person, or people the directly take care of the individual park you want to hunt, and ask, explain the tools and techniques you plan to use, you might have gotten a different response.

Public places, even private properties, in public view can be tough. You might get permission for yourself, but anyone seeing you swing, and has access to a detector, and a garden shovel, might get the idea it's okay for everybody.

For parks , find a lits of the rules on the internet or some other way and if there is no rule against detecting then go for it. Carry a list of rules with you if you can. But asking permission will unfortunately usually get you told no , even if there are no rules against it. Either they dont understand what you are asking or they dont understand detecting or they dont want to be liable for you or others safety so its safer for them to just say no. Be aware that even if there are no rules against detecting , there usually are rules about defacing or damaging property or harming the grass etc. and that pretty much covers detecting too. After doing the research on the rules if you still find nothing banning you from detecting , then do it but go at odd times when there probably wont be anyone there to question what you are doing and leave no holes or signs of what you were doing. Its usually better to ask forgiveness then it is to ask for permission. If you ask , and get told no even if there are no rules against it , you have still been told no which can be just as good as a rule. Ultimately the park is now off limits technically when you could have just gone and hunted to your hearts delight and probably never had a problem. You could always go anyway and hope nobody bothers you but your secrets out and somebody knows to be looking for you.

I wouldn't buy that response for a second. Sounds like a desk clerk who didn't want to put in the effort to look up an actual answer.