Fair point of discussion.
Let's look at the winners:
http://www.hockey-reference.com/awards/adams.html
Big names, who won it twice include Scotty Bowman, Jacques Demers, Jacques Lemaire and Pat Quinn. HOFers Al Arbour, Fred Shero and Glen Sather only won it once each. Among active coaches, Joel Quenneville only won it when he coached in St. Louis! Yeah, it's understood that the voting is completed before the post-season, but the man's won 2 Cups since. He must be doing something right in Chicago.
We can figure where Pat Burns fits in the grand scheme. It is interesting that nobody's won it twice since the last time Burns won it.
Edit: for argument's sake, a little research was required on the trophy.
http://en.wikipedia.org/wiki/Jack_Adams_Award
Although it is impressive to have won the award 3x, how meaningful is the award, itself? Are broadcasters really the most qualified to judge how good of a job a coach does? Many of these broadcasters would have seen little of the teams in the other conference. (Results are skewed toward the East.) Maybe there's no better way to guage. My first thought was to poll the coaches, themselves. Then, how to account for coaching changes during the season?