The case of Los Angeles gunshot incident

Kazuyoshi Miura was arrested for his involvement in Los Angeles gunshot incident. He was already not guilty in a Supreme Court decision.

US court said he was already not guilty because one incident is not argued more than once, but as to conspiracy he would not be charged by this so he ought to be judged in the US. They said arrest is just.

I think US can judge him in murder, or first degree manslaughter. Is US forgetting both US and Japan are different country? US court is acting as if Japan is a part of US even in judicial system. Though I can't deny Japan is already much involved in US political and economic system.