2 of her 3 trademark firearm patterns are currently standard issue for the US armed forces. I wouldn't call that "notably non-American", unless you mean country of origin, in which case she's Belgium-Israeli-Italian.
It's not unlikely to think she could hit up one of the several US military bases in Japan. They'd at least be ostensibly be better equipped and easier to find than the local Yakuza hideout.
langrisser said: The problem is that the fighters aren't American.
Remember that the series is in the not too distant future, meaning technology will be somewhat different in their universe.