Another detail sort of jumped into my head:
Is Kirk a reliable narrator?
We all know how common it was for Kirk to "Fogg up" his announcing duties during production of the show. He would frequently announce rooms incorrectly, among other mistakes.
That made me question just how reliable Kirk's story in the interview was.
Sure enough, I revisited the interview and Kirk "Fogged up" another story where he said (after thinking for a moment) a kid jumped out of the Cave of Sighs. We know that the kid actually jumped out of the Tomb of the Ancient Kings.
So we don't necessarily know if the player actually threw up in The Pit, and if they did, what season it may have been in. Kirk is not exactly the most reliable narrator.