Correct on all accounts. Just to be more precise, I'm not placing any blame on the players in my prior comments - the blame goes to GFN and Activision since the player expects to be able to play a game that they've paid for, on a service that they have paid for.

Yes and no, I don't know how GFN works, but as a Linux user I've heard enough stories of people being banned because they were using Linux because we get the game running in a "non-authorized" way, i.e. using something that's easier to describe as a windows emulator (even though it isn't an emulator). And the way to do this is enable the feature on steam for all titles, and click play on the game, so also people assume it's safe. This does not apply to CoD specifically, because it's designed not to work with that "emulator" purposefully, so I would assume that if GFN is in any way similar they would also have discouraged from using it.

No, it's a CoD anti-cheat issue. It shouldn't matter what platform you play on, you should only get banned if you're actually cheating.