I think that people are misunderstanding a few things.
1)Neither Pavel nor any Russians fans are saying that this Olympic gold makes Russia the best. What they are saying is that on a personal level, to a Russian, winning some domestic hockey cup, no matter how elite the competition, will never match up to winning Olympic gold for Russia. Especially when they haven't won gold since 1992. Especially when you are the Captain. Especially in this political climate. Achieving something for a corporate owned team is nothing compared to the honor of winning Olympic gold for your country. I think that last part is what really goes over people's head in North America. In America, personal achievement via some corporation is the apex of life. But what you must never forget is that to those that don't have the American mentality, Club Hockey is a business and Olympic hockey is a honored duty.
2)North Americans are really overemphasizing the prestige of the Stanley Cup outside of North America. No one outside of NA dreamed about winning it as a kid. Especially those of Pavel's generation. And when you start looking outside of hockey fans, 95% of the world has no idea what the Stanely Cup is, but everyone knows what Olympic gold is.
I think you are wrong about a lot of things in this post.
Not sure what you mean with political climate...especially with regards to hockey.
You really don't know Canadians then, winning a medal and representing Canada international is a huge source of pride for anyone who gets to do so. Whether the U18, U20, world championships, Olympics in men's and women's hockey or any other sport for that matter. Some corporate apex? Please...
Sorry but the Stanley Cup is the most prestigious team award in hockey when there is no best-on-best Olympics, period. 95% of the world does not know what the Cup is? Please, there is an estimated 7.6B people in the world, so 5% of that would be 380M. The US population alone is about 327M and I would guess at least half know what the Cup is even if they don't know every detail about the NHL playoffs etc. so that's 163.5M. Add Canada where everyone has heard of the Cup, 37M, and you are already at 200M even if you are really lowballing how many people of the about 880M in Europe and Russia that know about the NHL and the Cup, say 25% that's still 220M and you are at 400M without Asian, Australia, Africa, etc.
So the NHL and the Cup might not be the best known sport, far from it, but it's not as unknown as you say. Even among Canadian players, some find winning the Olympics a bigger deal than winning the Cup. Really ends up being an individual choice.