Another reply has already pointed out the "navigable airspace" limitation. The specific FAA rule is FAR Part 91.119 Minimum Safe Altitudes. Basically 500 feet everywhere, and 1,000 feet over "populated areas".
Back in 1981 the FAA addressed RC operators with Advisory Circular 91-57. It requires RC operators stay under 400', remain in line of sight, and coordinate with an airport if they are within 3 miles of the airport (which is where planes may be under those minimums due to take offs and landings.
This set of rules basically insures vertical separation of RC operators and "real" planes. It's worked for over 30 years, quite nicely. In fact the FAA is quite happy with this for "drone" (really RC quadcopter) operators. Buy one, fly it over your house within the rules, take a video and post it on YouTube for your "hobby" and the FAA is perfectly ok with it, and won't give you a hard time.
Rather, the FAA is drawing a different line here. They have a long history of distinguishing between commercial and private operations, and have different regulations for both. They have generally held in the past that "all commercial operators must be licensed", which in the context of real planes makes perfect sense. But with these new quadcopters this rule has gone screwy. If you take the same video from the last paragraph and provide it to your realtor to help sell your house, suddenly you are a "commercial" operator and can't operate without an FAA License, and oh by the way they have no procedure to license RC operators right now so you can't get one, but you can ask for a one off waver, it may be approved in a few months.
And that's what is stupid here. If it's a RC device, operated by a human, under 400' and in line of site, they should stay out of it. Commercial or hobby shouldn't matter.