You said "A winning culture doesn't win you Cups. Winning Cups produces a winning culture." What you typed in defense above does not prove your statement at all, for several reasons I don't feel like laboring through, not the least of which is that bringing in one player is not proof that a change in culture has taken place.
If you want to just isolate your perspective to the Subban/Weber trade, that's a different story. But I'm not responding to that. I'm responding to your generalization about winning cultures happening before or after championships. Any sports psychologist, coach, or athlete who has the least bit of high level experience will tell you otherwise (and that doesn't mean they never rely on stats, just that they understand psychology and managing the culture beyond stats). Whether or not moving one player changes that dynamic completely is another story.
I brought up the topic in response to some people here wanting to ship out Backstrom or Ovechkin if they fail again this season due to them being "damaged goods" or similar. They're only damaged goods because they haven't won a Stanley Cup, not because there is something inherently about them that makes them losers. Shipping them out for "proven winners" would be a catastrophic mistake unless these "winners" are actually better players. Did the Penguins really win the Cup this season because of a winning culture? Or was it because of good players, coaching, and puck luck? I'd heavily lean toward the latter.
The media (and coaches, players, etc.) only speak of a team or player having a "winning culture" after the team or player has won a Stanley Cup or other championship. Think of the Red Wings in the early 1990s, and the 2010s Blackhawks and Kings. Before they went on to win their Stanley Cups, these teams were thought of as perennial losers and no one spoke of them being winning organizations. Yzerman in particular was branded a loser, until he won, then he was a winner. Funny how that works. And did these teams undergo some sort of big culture change? Maybe slightly? But it's far more likely that better talent, better tactics, and some good fortune turned these teams into "winners" rather than a culture change.
Did anyone speak of the "Patriot Way" before they won their first Super Bowl? Isn't it much more likely that Bill Belechick's tactics (especially defensively) and Tom Brady's talent were the reason they won all of those Super Bowls, and the whole Patriot Way thing happened after they won?
"Culture" is just a buzzword IMO. It doesn't have any real value and is mainly used to explain away things that hockey executives have no clue about. I'm sure some coaches, athletes, etc. say it's important, but that doesn't make them right.