Let's see if we can free you guys from the Dalli Loop.
You are making a presumption that the game has a single, universal state for all playthroughs, and base your "If there's no STD on Jill path then it's not present on all other paths, either" conclusion on this.
But, while pretty reasonable, it is just a presumption. It's perfectly possible for the developer to do a "butterfly effect" of sorts for their game, where the state of the game is subtly different for each of the potential LIs. In such scenario what happens in path for one LI isn't a proof for another LI's route. And i think that's where Dalli is coming from -- you're presuming that there's one universal state, and he doesn't.
Only DPC knows which of these is actually correct, so best just agree to disagree.