I put this chart together using penalty data from nhl.com from the last 10 years to take a look at "game management" in the NHL. It's obviously a very basic analysis for a complicated (alleged) issue, but the correlation is also incredibly high.
If reffing were purely objective, you'd expect there to be a weak relationship between penalties drawn and penalties taken. There could still be some correlation, because if one team is being aggressive and dirty, it can tend to bring out that same behaviour in the other team. Regardless, over a full regular season, you'd expect that a "dirty team" would be penalized far more than their opponents, and a "clean team" to be penalized far less than their opponents.
Above is date from 2010-present, 10 seasons (with the asterix of 2013 being lockout shortened, and this season being only partially completed). There is a VERY strong correlation, R2 value of 0.912 for those of you that know basic statistics. To me this absolutely screams that refs are interfering in games on a very very regular basis. Rather than calling games objectively, they constantly do "make up calls", and try not to "interfere" in the game too much.
I.e., if one team is dirty and gaining a lot of penalties, they'll make a bunch of softer calls on the other team to "even things up" (this represents the higher end of the distribution where teams with a ton of penalties for also have a ton of penalties against). On the flip side, cleaner teams, because they commit very few penalties, will have very few penalties called on their opponents regardless of how the opponent is playing, allowing their opponents to get away with what should be penalties (see low end of the distribution).
This creates a situation where refs aren't calling penalties objectively on both teams, but are instead constantly shifting the goalposts, and creating different standards for different teams.