I'll chime in here... and I have to say adam is on target with my personal experiences.
I live directly beside a very historic national park and cemetery- in fact, it is possibly the most photographed, and most bucolic piece of parkland the entire portion of the state has to offer- and it's significance in American history is undeniable.
Rather than just make assumptions, and plan on begging forgiveness instead of asking permission, I made a formal visit to the ranger's office, and spoke with the hmfic. I was told in no uncertain terms that what I wanted to do was formally against the rules- and they were amateur shutter bugs themselves and had recently looked into some similar plans, so the word was fresh from higher up.
Now, they did not need to do the next thing, which was gently imply that if I happened to know anyone with property adjacent to the park, then I could always fly from there, and there happens to be a lot of adjacent, privately owned land as it is all farm fields surrounding the specific areas of photographic interest.
I can say that I have blurred the line, and broken it over time, and there have been no repercussions or even a hard look. I am sure that should ever I do something foolish, or unsafe, or disrespectful, then I will have a hammer come down. I am grateful for the long leash I am currently given.
The reason I was able to pull this off- and if I can get a major upcoming yearly event, as well as some other footage before, and if the worse should happen, well, that is forever, and NOBODY has footage like I have from such awesome low altitude angles of much of this area- a handful of panoramas and pics from airplanes and helicopters- real ones, and that is it. I would have a major score for my personal collection. Back to my point- the reason I was able to do all of this was my approach- I was respectful, let them know who I was, and that I understood that there could be boundaries, and that I wouldn't take advantage of any courtesy shown me in any blatant fashion that would directly reflect on them, and their job and responsibility- you see, that is what matters- covering your ***... and that is what is paramount in those ranger's minds- they cannot be perceived as allowing anything unsafe on park property. We need to truly acknowledge that.
The old saying, "You get more flies with honey than you do with vinegar" will always hold true.