Pinoko's fictional backstory in "Pinoko's Mystery" is her real backstory.In other words "Pinoko" is really Miya, the time-bomb mechanic's kid who nearly died in a freak explosion. Her mom took her to Black Jack, who lied and said that Miya died on the operating table. After her mom left, Black Jack rebuilt Miya; when Miya regained consciousness, he took advantage of her amnesia by lying about her origins, and renamed her Pinoko. Creepy, but makes more sense than the Fourth Wall Ass Pull the story ended with. It also explains why Pinoko's psychic powers "disappeared"—she never had any to begin with.
Black Jack and The X-Files take place in the same universe.Like Reality Unless Noted? Check. Paranormal phenomena? Check. Corrupt authority figures? Triple check!
Black Jack has the Healing Touch.How else would he be able to perform such crazy operations? Doctors have noted how quickly he operates, as well; maybe he even has the same Healing Touch as Derek?