Sorry, but this is not true. Airspace above private property is considered public right of way, in the same way that a sidewalk in your front lawn is public right of way. The ceiling of what belongs to the landowner is a gray area of law, but is generally considered to be the space that is actively used. If you have a trampoline, for example, then your active usage is slightly higher than that of your neighbor without a trampoline.
The FAA operates under a white-list. Everything is illegal until a regulation is made to make something legal. Radio-controlled aircraft have an exemption for recreational flight. Unmanned aircraft operated for recreation fall under that same exemption. For commercial, or civil usage, a certificate of authority (COA) is required on a per-case basis since no blanket regulations exist yet.
"That poses the question whether we are within our property rights to shoot down any drone flying around inside it?"
No. If someone drives an R/C car along the sidewalk in your front yard, you are not entitled to shoot it because of your property rights. At best, you could try to prosecute for trespass. Same with a flying vehicle, but unless the flying vehicle is under 20ft or so, the odds are not in your favor.
The other interesting question which has yet to be answered is whether laser damage to video sensors in an unmanned vehicle in the landowner's "airspace" is actionable.
The final interesting question is whether or not its actionable if your R/C plane that you were flying around on your land and it happened to run into a drone and both fell out of the sky is a problem for you or for them. (I'd start that one off by suing them to replace your airplane)
I don't doubt though that all of these will be tested in court though.
The reports of 'celebratory gunfire' deaths are all necessarily speculative - the angle of the shot is impossible to measure. We can resort to physics to get a better answer than that derived from headlines.
A close friend of mine was killed by a stray bullet this year at a 4th of July celebration. She was in a crowd of thousands of people gathered to watch some local fireworks. The shooter was miles away and probably has no idea that they murdered someone.
http://statenews.com/index.php/article/2012/07/student_shot_...
Seems like they should have a warrant if they want to operate drones on my property.
Drones don't appear to be covered by the public domain airspace laws in the US: http://en.wikipedia.org/wiki/Air_rights
Airspace under 500' AGL is traditionally considered to be under control of the landowner - unless they are near an airport and the airport needs right of way for passengers. While the FAA technically controls ALL airspace, they can only use it for right of way purposes when dealing with passengers. It doesn't appear to be valid for unmanned aircraft.
The FAA has a few things to say about drones here: http://www.faa.gov/news/updates/?newsId=68004. There doesn't appear to be a specific drone law in place by the FCC, only waivers to allow flying the drones by an agency.
That poses the question whether we are within our property rights to shoot down any drone flying around inside it? Given the FAA is limiting these drones to operate below 400' AGL, they would appear to be a fair target.