Unfortunately, I have to say the assumption that gaijin are committing more crimes than Japanese is probably correct. While that sucks big time, and I'm affected negatively by it, it seems like gaijin crime rings (generally people from the Asian continent--Persians & Chinese being the worst culprits) do exist. Of course, I have no proof other than what I see on the streets of Shibuya, Shinjuku, etc.
But it's true that the media DOES sensationalize gaijin crimes more than Japanese crimes. I saw a story on the news once where a Chinese was suspected of murder in Japan. Instead of calling the suspect "Chinese", they just called him "gaijin". That pissed me off, because it perpetuates the mode of thinking that gaijin are all in one category without distinguishing us by nationality or race.