To be honest, the answer is yes, you're correct. But you don't need any complicated or fancy reasons for it like you have. Nearly every video game series is connected to nearly all other video game series in extended canon. And it is almost always "cop-out explained" away by dimensions. For example, Mario has the ability to hop between them.
The Infinity Ward Call of Duty series is connected to the dimension of the "Real World" via Tony Hawk skateboard crossovers.
The "Real World" is connected to the Mario series via Punch Out (versus Donkey Kong and Mike Tyson) as well as many other crossovers.
The Mario series is connected to the Zelda series via appearances in each others' games.
The Zelda series is connected to the Super Smash Bros. series by self-explanation.
The Super Smash Bros. series is connected to the Pokemon series by self-explanation.
The Pokemon series is connected to the Elder Scrolls series by various subtle Pokemon references.
The Elder Scrolls series is connected to the Indian Jones series by more subtle references.
The Indiana Jones series is connected to the Treyarch Call of Duty series by crystal skulls.
The Treyarch Call of Duty series is connected to the Rising Dead Zombies series by the Ray Gun and Gersch Device.
The Rising Dead Zombies series is connected to the Infinity Ward Call of Duty series by characters, campaign, gun, etc.
And now we're back to the beginning. You can expand this into a complicated web, so you can say pretty much any character can be in any game through extended canon. And this is true with real life too. In an expanding multiverse theory, literally anything that could possibly be is out there somewhere. So, somewhere, in real life, in another dimension, Samantha rules. Aliens run amuck. And a plumber eats mushrooms.
According to inter dimensional theories anyway.