The rejection of QC for expansion has been widely speculated it was for 2 reasons. 1) The Canadian dollar. 2) The NHL knows a team (or teams) will need to be relocated and there are not many cities with an ownership group and arena ready to go.
Regardless of the reasons (all of which I was aware of), your comment about it not being up to Bettman in terms of expansion/relocation, though not completely wrong, was speaking in absolutes, which was. No one said Bettman holds absolute control of such decisions, but it's undeniable he's got a strong influence in such decisions.
The point of bringing up Quebec was simply to point out that the NHL had denied Quebecors' bid for expansion (again regardless of why). While Bettman would not have made this decision by himelf, he absolutely would have had some say.
And no Bettman isn't a large part of it. The BoG is the large part of it. People still talk like Bettman hates Canadian teams, but the reality is he saved Canadian teams, without the way he has guided the NHL would only had 2 or 3 Canadian teams. I really think this perception that he doesn't want Canadian teams is skewed and inaccurate. Would he prefer a place like Houston, Seattle or Portland? Probably, but that's not because QC is Canadian, it's because it is a smaller market. The league will only really grow by breaking into the largest markets possible. Canadian teams, while they will get support, that fan base doesn't really have the potential to grow as much.
And who largely makes up the Board of Governors? The owners. And who does Gary Bettman work for? The owners. There's a valid reason why the majority (if not all) publications that release "power rankings" of NHL related figures have Bettman at #1. He has influence in every decision the owners make.
I'm the furthest thing from a member of the "Bettman has an anti-Canadian agenda". It's simply not true. But Bettmans' job is to (1) make the NHL more profitable, and (2) to grow the game (which is largely because growth of the game will have a significantly positive impact on #1).
Beating the dead horses that are the Arizona Coyotes, Florida Panthers, and Carolina Hurricanes hasn't made the NHL more profitable, as a relocation likely would. The only argument to be made that an NHL team had influence in Arizona, is that hockey is probably gaining popularity there, but hasn't resulted in making the NHL more profitable.
Which is again, the point of my first post, that even a small Canadian market would be more profitable than a couple of the American teams. It's purpose was not to push the "Bettman has an anti-Canadian agenda" narrative.