I was actually riffing on the Evil Demon thought problem of René Descartes. But you could also make it the "Brain in a Jar" problem is you prefer. Essentially: Everything you see is an illusion created by someone else and there's no real way to discern that false reality from a true reality.
Which means both scenarios happening at the same time is not a problem, since each side is experiencing their own, unique, hallucinations which do not need to share the same details in any meaningful way.
I still think the truth is gonna be closer to "Bad Writing" with no further explanation, but it's not like this philosophical problem hasn't appeared throughout the media for over a decade. Everything from Buffy the Vampire Slayer being convinced she's not -really- a vampire slayer and is actually a girl in a mental institution, to Captain Ben Sisko being coached to believe that the entire plot of Deep Space Nine was just a story he came up with, to the entire goddamned PLOT of "The Good Place" being literally about evil demons manipulating a person's perceptions of reality to convince them they're not actually in Hell.