If they deny you should get it in writing and make sure to get them to note why as well as what can be done in the future to avoid this.
Good luck with that. I have written to a local airport and local FAA office on much more important safety concerns in the past (non-drone related). They do not respond. If they stay on the phone long enough to hear to request for written response, they will probably laugh at you.
While there are absolutely some valid safety concerns at play, the entire concept is ridiculous for what I would guess is 99% of situations. The hospitals, heliports and small private airstrips likely feel they have much better things to do than field phone calls and write letters for "some kid who want to play with a toy in his backyard." The system was not designed with the current situation/technology in mind. Something needs to be done - quickly. Our FAA has their collective heads so firmly up their back-ends that they can see sunlight out of their own mouths.