It's always easy to critique an action or behavior after the fact, especially with all of us calm and sitting in front of our computer screens with plenty of time to ponder. My comments will be made with this disclaimer in mind.
I would have complied with the officer's request with a statement like "I'll land my drone and comply with your request, but I would like to discuss with you my legal actions". That verbiage would've gone a long way towards disarming the law enforcement officer (-He truly thought you were violating the law). Then I would've entered "Columbo Mode" (-remember the old TV series?). I would've continued with, "I'm sorry officer, but I try to carefully follow the law precisely when it comes to flying my drone, and from my research, it's legal to fly here". "Can you help me with the specific statute so that I can share it with my drone flying club?"
From there, the conversation would've progressed in a less dramatic nature. The officer's reference to manned aircraft could've been countered with "You know, we looked at that regulation and noticed that it was directed towards manned aircraft. Hobby devices, like drones, according to the FAA, fall under completely different rules and regulations, and our state presently has no direct rules governing flying in State parks. -That's why I'm here. -But again, I don't want to violate the law and do something inappropriate. If you could help me find a regulation that I could share back with my group, you would help all of us". "Do you have the time?"
I've actually used that type of approach before with a very positive response, and to the point that I let the cop "autoland" the drone. -Even sent a copy of the footage by email to him and the City. By doing so I made a friend, and I'm welcome back in the city, and to the point that we've discussed drone do's and don'ts. There's still a very real concern by law enforcement centered around the potential danger that a drone can inflict. That's where law enforcement feels that it's their responsibility to protect its citizens. Ironically, I'm now included as an "expert" in their discussions.
Being handcuffed and placed in the back of a patrol car is not "winning". Now the paradign has shifted from enforcement, to justification. The officer must now legal justify what he's done, making it difficult (-if not impossible) to go back to the discussion stage. The same with the legal entity governing the park. They now have written an adverse rule that affects future drone activities, effectively buttoning up any future flights. In their mind, the "danger" has been eliminated. It could've turned out differently, don't you think?