I'll argue that the police can enter the park with their vehicles, but they'll be violating the rule when they do so.

But if we're ignoring local rules and the only question is whether or not they would be violating the rules, then yes they would be, and whether they can anyway is out of scope.

Yes, exactly my interpretation - which makes this a rule violation. Whether this rule violation should be persecuted is a different matter though :)

In that scenario the duty to help citizens in need simply supersedes the rule that vehicles are not allowed in the park. So pedantically the EMT and police officer are breaking the rule, but breaking the rule of idly standing by in an emergency is worse.

The reason to allow emergency vehicles to go through the park must then outweigh the benefit of the ‘no vehicles allowed rule’. Something trivial like a pedestrian illegally crossing the street should not warrant the police going on a car chase through said park.

Yes, I'm not questioning whether in real life this sign would cause issues or not. The question is "Does this violate the rule?", To which the answer is "yes" for an ambulance.

Whether it's fine in certain scenarios to break some rules it's a different topic though.

Whether it violates the rules depends on whether you live by the letter of the law, or the intent of the law. When it’s by the letter an ambulance is obviously violating that rule but that’s perhaps not the most sensible way of going about things.

> The reason to allow emergency vehicles to go through the park must then outweigh the benefit of the ‘no vehicles allowed rule’.

Exactly, the Hippocratic oath supersedes the no vehicle rule.