That being said having a photo of your passport and relevant stamps is good advice, but only to make it slightly easier to deal with all the hassel that comes if you do lose your passport.
Note that this doesn't include your passport stamp pages but Japan hasn't issued passport stamps for several years now and they just look up your passport in a registry instead. So for that purpose, a true copy should be effectively the same thing.
That's where it comes down to what is essentially a technicality but given they carry an embossed seal and signature with the words "TRUE COPY" on them, they look very official and officials are very rarely going to push back on it even if whether they are to be treated as a full substitute for a passport (for identification purposes) is technically a grey area.
Unless you are involved with a particular interaction, they just want to check your visa status. A passport photo/stamp will do if their system is digitized. Arresting someone (except for the US where the police likes to arrest people) is a major hassle.
To csomar: you are willingly spreading harmful advice. Stop it. Stop making people reply to clean up your mess.