10,000 Okinawan men. Overall, American troops are 86% less likely to commit crimes than Okinawans. So, to echo what Michael Whalon says, the conduct of United States military personnel in Japan is extremely correct, at least as far as the cold hard statistics are concerned.
Anyhow, the supposed predilection of American forces for criminal behavior has nothing to do with why they are there. The US presence in Japan is to help defend the nation against potential adversaries China, North Korea and, until 1991, the USSR.
Also, it's kind of rude to characterize American forces in Japan as "foreign contamination and intrusion". American forces aren't some sort of biohazard.