I don’t for a second think it’s rigged like say WWE where it is scripted. But I do believe there is influence to have Canadian teams (all of them) not win a Stanley cup. Way too much bias officiating when a Canadian and American team meet in the playoffs to ignore. Again not just the Oilers all Canadian teams. I remember last year or the year before where they showed a graphic of the comparison between Canadian based teams and everyone else and it was practically 3:1. You can’t fully rig a game but you can definitely influence it with that kind of mismatch.
It's rigged in the sense that officials don't referee the games they manage them. The league wants close games without the appearance of interfering with results, there's likely quite a few things that are considered such as:
1. The importance of the game
2. Current Score
3. Quality of PP
For some reason there is also still a belief that calling penalties when they occur is the referee influencing the game and that they want the players to determine the outcomes. And that's not just in the league that's with a huge number of fans as well.
Hard to find thorough details to check the balance in match ups between US and Canadian teams, though in general the only Canadian team with a positive penalty differential are the Leafs, the rest of the Canadian teams are in the bottom 10