I think there are few overlapping concerns here and the 'drone photography' is just a shorthand.
1. Public works of art (sculptures, etc) are absolutely covered under copyright law; I would assume garden design could arguably be as well. Architecture isn't, but the org very likely has a valid claim not to allow 'commercial use' A/V of the works on their property, regardless of the device used to capture it or where that device is in space. Many cultural heritage sites across the world similarly don't have a huge problems with iPhone photos, but once the full frame DSLR and tripods come out the org's assumption is 'you are doing commercial work'. Some orgs are of course more strict. you can't take a photo of the ceiling of the sistine chapel with your phone without getting yelled at because of the Vatican's agreement with, Nippon TV. You could of course try to argue that you are only using your footage for fair use/educational purposes, or if you are an artist or social-commentator yourself you could argue maybe you are planning on significantly altering the footage to make a derivative work for satire or otherwise notable public comment, but for all that trouble you might as well just talk to them and put in the application.
2. As with tripods and other possibly large commercial setups/rigs, they are concerned about the possibility of an uninsured device falling out of the sky and striking a patron who in turn sues them, not you. Page 3 of their policy speaks directly to this in the broader context of commercial use.
They probably could care less if you fly over at max altitude in passing, but you should contact them with your particulars.
jrupprechtlaw.com
