The police can interpret the law one way, place you under arrest, they just need probable cause. The city, district, or state attorney will determine if there is sufficient evidence, or if there was potentially a law broken, and decide if they want to move forward, and charge you with a crime. At trial, you get to present your case, a judge and jury determine if you broke the law, and need to be punished for it.
The courts are pretty busy with more serious crimes, not too likely you are going to trial for digging pulltabs at the park. But, you do get a little black mark on your arrest record, although many lawyers can help you get it removed, least from public view, after a year or so, if the charges are dropped, or you win your case. If you have to avoid the park workers, that pretty much acknowledges you know that it's wrong. Talk to the park workers, if they don't see a problem, you don't have look over your shoulder, or watch the clock, to get out of there before they arrive for work. Not what I consider fun, but some get an adrenaline thrill, getting away with such things.
Can't imagine a city, with absolutely no other alternatives to hunt in public. Sure, some people are a little shy, don't express themselves well, so avoiding the things the fear, like asking permission, rejection, is the only option. Maybe this one park is, the someone most popular with the 'friendly' old guys, who will walk up to most anyone, one hand thrusted deeply in their front pocket, searching for something... I had to stop taking one of my dogs to a park like that, he knew I was a little annoyed, and was shy about expressing it. Usually a friendly, and well behaved dog.
Each site, is individual, some of the folks caring for it, maintaining it, might have a problem, and tell you know. Some might not really care, long as they don't have to clean up a mess. Some could be into the hobby, and interested in what you find. Never know, until you introduce yourself, explain what you plan on doing. Even if there are rules, they still oversee the individual site, and make an exception, unless it's clearly posted on a sign, that metal detectors aren't allowed.