The OP mentioned at no time were they touched, searched or otherwise harassed, far better than what the TSA does.

Fake police might of hassled for money or other items, the incident described by the OP doesn't sound out of normal to a stop conducted by a regular uniformed officer. Since nothing was amiss, no formal report was needed, thus no need for him (the officer) to copy detailed information from the passport, other than some notes into the police notebook, which officers carry. Japanese bureaucracy... trust me if something was amiss a lot of detailed paperwork would have been done.