I don't think SpaceX is really seeking attention. They don't depend on consumers or the aerospace industry at large. Musk certainly doesn't strike me as the kind of person who craves attention. The interview on the Daily Show was the first I had ever seen with him.
They definitely do some amount of PR - in addition to Must going on Jon Stewart he also did a great interview with 60 Minutes earlier this month.
Although they don't directly need consumer support, getting your name out there helps with recruiting the best engineers. I know several people who were tops in their field and heard about SpaceX, dropped what they were doing and applied.
It also helps them with public support. It's very possible that the majors will come in and try to use lobbying to crush SpaceX. Having the public on your side will help SpaceX beat that back later.
