You can shoot someone else's gun the range etc, as long as you are legally in the US. I know I have taken foreign friends to the Police Range in VA.
I know I wouldn't have any problem letting someone from Japan shoot my guns at a range with supervision. My experience is that people from Japan tend to be very respectful and follow directions - two traits that make it easy to teach someone how to properly use a firearm. Personally, I'd love to see tourists from other countries come here to indulge themselves in learning to shoot various firearms. Drop the kids off at Disney World and off to the shooting range!