Am I literally walking through federal airspace right now?
The U.S. Constitution is pretty explicit about physical space that is allocated to the federal government and the reasons (post offices and post roads, military installations, and that's about it), so laying claim to every square inch of "air" above that land seems to be quite a stretch.
This issue has been settled for quite some time in US law. The main grey areas that exist are debates over what sorts of exceptions should be made for reasonable use of UAV/drones at low altitudes.
Would flying a drone indoors require permission from FAA? What about a daredevil jump on a motorcycle?
As for airborne ground vehicles - it's difficult to imagine a situation where it would legitimately be a concern, which is why it's a grey area :)
That does mean technically that if you're flying a drone indoors, the legality depends on how wide you open the windows.