Uh, as someone who *does* have a pilot's certificate, the GP is more right than you are.
First of all it's a certificate, not a license. Yes, the distinction matters. And there's lots of not-commercial aircraft - in any case the airspace rules are no different.
You don't own the air up to 500 feet by any means. The FAA's rules (mostly for fixed-wing aircraft) are in 14 CFR 91.119, paraphrased:
- Always where an emergency landing can be conducted without "undue hazard" (note, not "no hazard") to people or property on the surface
- Congested areas, like towns and other areas the FAA decides (naturally only after they come after you) are "too populated", like highways. 1000 feet above the highest obstacle within 2000 feet. At a minimum, includes the yellow areas on the World VFR chart here.
- "Other than congested areas", but not "sparsely populated" - that's your 500ft rule
- "Sparsely populated areas" can be operated arbitrarily low (subject to the first rule) as long as they're 500ft away from person, vessel, vehicle, or structure. This is why crop dusting is legal.
Of course this obviously doesn't apply to takeoffs and landings. It also doesn't apply for helicopters (they have a looser set of rules) and a few other kinds of aircraft.
The long and the short of it is I can fly over your field at 20 feet all day long if I want to. It's not very courteous, but it's quite legal. I can fly 501 lateral feet from your second-story bathroom window, even if it's over your property. And of course a helicopter can fly lower and closer than that, even over a congested area. Again, not courteous and not necessarily smart, but there's a whole lot of things in flying that are legal are not good ideas.
You have no special sovereignty over the air above your property. You can use it to the extent the use is reasonably connected to the property below. For instance you can put another level on your house without asking anybody, or even a tall radio tower (>200ft or near an airport you have to tell the FCC), but you can't put up a "spite pole" just to keep airplanes away. So basically you have a right to your airspace to the extent you don't try to exercise control over it by excluding airplanes.