Season 1 episode 8 (IMDB), episode 9 (Paramount), or episode 11 (Memory Alpha). Anyway, we get a complete copy of Earth, the failed longevity experiment, bonk bonk, and Kirk wrenching a kid off a desktop. Beyond that, no explanation surrounding AN EXACT COPY OF EARTH! Zero, zip, zilch, nada.
Side query: What’s considered the “official” episode breakdown?
I think this is one of those things that Kirk likely stripped from the log, since just showing up there clearly violated the prime directive. Without any record, there would be no way for the rest of Starfleet to know that planet was like that which would also reduce the likelihood of another ship visiting.
I definitely have the head canon that Kirk likely was especially bad about leaving stuff off the record, which explains the frequency of mostly trusted bridge officers going on away teams.
Anyway, the Enterprise crew wanting to gtfo as soon as possible is probably why we don’t get more answer, and if there is no report to Starfleet, no one else would be compelled to investigate, which leaves us with as few answers as Starfleet.
I know this is almost purely speculation, but that’s what I think went down.
The only bit refuting that is the brief discussion about sending teachers and, according to Bones, “truant officers” to the planet after they leave. But then, all of that could be attributed to Kirk’s exaggerations.