No, I've seen a coach or two fired or resign for winning the league but losing both games to their top rival. Or losing a knockout game to a rival despite winning other trophies. It's not a guarantee and many survive that, but fans definitely start grumbling about it when it happens.
that's what I sort of thought you were saying. My only exposure to any of that is playing Championship Manager for a bit and being surprised at how strongly the board of directors acted when I lost to a rival. In EHM (same developers), they'd never do that.
I think a lot of it comes down to how large the coaching field is perceived to be, and how similar the game is played pretty much everywhere. A Premier League team can recruit from Italy, Spain, Portugal, France, Germany, etc., in addition to domestically. NA hockey isn't like that. IIHF rules make the game different enough that we don't trust the results of the KHL, SM-Liiga, SHL, etc., which makes our world much smaller.