I'd venture a guess that any "pilot" safety problems with GA aren't the fault of the FAA, flight schools, or most pilots. It's the simple fact that in all actuality there's no real standardization between sources of flight instructions. What this leads into is a variety of individuals with various levels of judgement getting into the cockpit. I've long maintained that it's no great feat to teach somebody to fly. To allow somebody to gain the type of experience that produces good judgement is an entirely different proposition. Think about it - a newly minted private pilot with 50 hours is allowed to do pretty much anything in the air, given a simple enough aircraft and no flight into IMC. Then again, consider the number of accidents from low time pilots that resulted in the pilot being overconfient in themselves, their aircraft, or were simply doing something that was, for lack of a more accurate term, stupid. It seems to me the FAA (or somebody else, I can't quite remember) did a study a couple years back to find out how low a private pilot without an instrument rating would typically do in continued flight into IMC. The answer was that unless they immediately executed a 180-degree standard rate turn, they'd crash due to controlled flight into terrain in an average of 178 seconds.
The point to my little rambling diatribe is this: there's a difference between the ability to control an aircraft and the ability to consistantly make good decisions from the left seat. The press however, dosen't know or care about this, so every time we have some idiot on TV like the whole Jessica Dubroff fiasco, kid-ignoramus flying into a skyscraper in Miami, or just a spate of GA incidents, the press decides to tell America that GA is inherently unsafe, when in reality the incidents are the result of a few pilots exercising poor judgement and falling victim to the aeronautical equivalent of natural selection because of it.