"nobody takes anything that doesn't belong to them" is quite the stretch. It's true that people don't tend to steal and that things dropped on the street are often treated as though they should be returned to the rightful owner but that is not 100% the case. Like in the US there are "good" people and "bad". Also like in the US there are those who are "good" when others are looking and maybe not so "good" otherwise. Also I have seen wallets etc. handed to the police in the west so it's not a uniquely Japanese thing, although maybe the likelihood is indeed higher in Japan.

Also, the cost benefit of 1jpy vs having the chance to impress a friend is quite low. It would be interesting to see how your friend would react to seeing a 10,000jpy note on an empty street walking home one night when nobody was looking. Maybe she'd "leave it for the rightful owner to come back and get it". But maybe not. Different cost benefit analysis in that case.