And she would be right.
PCs and NPCs aren't fixed, real objects that can only exist in one imaginary world at a time.
Saying, "This is Gorax the Destroyer" doesn't mean Gorax the Destroyer has just vanished from another game to appear in yours.
Ah, there's a difference between us then: to me there's only one Gorax the Destroyer, and if he's bashing around in my world he can't simultaneously* be wreaking havoc in yours. And yes, if the Gorax from Speiadeia in my world just appeared in your world, that by extension has to mean he just - somehow - disappeared from my world.
* - the exception being if Gorax has been cloned, but IME that's pretty rare...and clones tend to want to kill each other anyway if they exist simultaneously.
Gorax the Destroyer can exist in any number of imaginary worlds simultaneously, and it does not create any kind of temporal rift, it doesn't threaten the stability or authenticity of any of those worlds, and the use of the character in one world has no bearing on it's use in the other.
Well, yes it does if there's only one Gorax.
It's a question of treating the characters as if they are real people.
To suggest that using a character in one game has an inherent, actual, real effect in other gameworlds, and that this effect occurs without the permission or knowledge of the participants in that game makes no sense.
I'm saying instead that it in fact does make sense that such cross-world effects can happen if-when characters jump worlds, and that it's unethical to do things that would cause those effects without the permission of the affected world's DM. Again, it just comes down to asking permission - and not being an asshat if said permission happens to be declined.
If the participants continue to imagine that Gorax is in their world, and only in their world, then within the shared space of their game, they are correct.
Except either the imagination of those people or the imagination of the other people is now based on an error, as (barring some really twisty-bendy in-game physics!) Gorax can't be in two places at once.
Nothing anyone else can do will change that. The only people that control what happens in the shared imaginary world of an RPG are the people particpating in the game. No matter what things you choose to imagine in your game, my game is unaffected.
In which case one table or the other isn't being true to in-game causality.