To be fair, legal and unlicensed powered paragliders are able to reach those heights[1]. I only know about airspace classes by way of Wikipedia, but it seems like anything below 18,000 feet and far enough away from an airport in the US is fine.
Indeed the problem was that he didn't establish two-way communication with air traffic control. Historically, VFR flights inadvertently straying into a terminal control area have actually killed a few hundred people, so it was reasonable for the FAA to fine him.
[1] http://en.wikipedia.org/wiki/Powered_paragliding