There is a slight slant towards North American players in the NHL, though. Don't get me wrong, a good enough player's going to make it no matter where they come from, but on average an European in the NHL tends not to be a depth player. This is due to the fact that after the sharpest tip, there's a wide pool of players to be used in the lower echelons, and GMs tend to favor North Americans for those roles - simply for the fact that it's far more convenient to use domestic guys than haul in foreigners to play in the 4th line. If an European wishes to break it, he must bring something truly special with him.
Also, the slots in the NHL aren't limitless. 20 players across 30 teams is only 600 players. Even if you count the depth options, only around 700 players on this Earth can call themselves NHLers any given night. That's actually an extremely small number when you think about it.
And by statistical probability alone there are bound to be more good players worldwide than just that. The NHL possesses most of the sharpest tip, no doubt, but there are bound to be plenty of players in the Euro leagues who could go head-to-head with NHL 3rd liners. The fact that most North Americans have never heard about them does not make 'em any less of a threat.