"non-residents": Did you mean non-citizens? Else, I do not understand the context of this term. Clearly, the OP was talking about living/working in Japan. That would imply residence. Yes, there is national health care. For working age people, it costs about 10-20k yen per month (many factors can change the final cost). Co-pay is 30%.
It's actually better in practice because the state puts maximum prices on all kinds of procedures, and IIRC there is also a maximum annual amount that you can be charged. IOW it's easy to ensure your care costs are bounded.
Great point! First, I didn't know that the national gov't is actively involved in medical pricing. I guess it makes sense when you have national health care. Second, to state the obvious, 30% would be insane co-pay for someone in the United States. However, in Japan, it is quite reasonable. Elderly only pay 10%, and most children pay nothing.