I don't think the players think that they "deserve more than the other leagues." I think it's a question of the players getting what they think is "fair", and that the 57% is really just a number that people are too hung up on. I think that there is still a great deal of mistrust on the player's side, and that they really don't think that the owners are as in bad a shape as they claim to be. Heck, as recently as May Gary Bettman was boasting about how great revenues were and how high attendance was and how fantastic the new TV deals were going to be. Check out the quotes from Bettman that Alan Walsh keeps tweeting, about how the "new partnership with the players" was so great for everyone.
Then consider all the recent signings, including Marchand and Seguin's signings this week. Or of course Minnesota's big splash, or Philadelphia or, or, or. Actions, as they say, speak louder than words. If the money was not there, then they would not be spending it. Right?
Now go back in history. By all accounts (at least at the time and up until, oh about three weeks ago) everyone said the players got hammered in the last lockout. They were humiliated and embarrassed and they ate their own right after, so disgusted were they with their own performance in the whole matter. Now people are saying they need to "give again". They must be thinking "weren't we humiliated enough?" Whether you NOW think that is true or not for the last seven years that has been the general perception.
Now keep going back. Remember the Levitt report and it's, ummm, "creative" accounting? Remember the Blackhawks saying that they were still losing money? Or the Habs claiming they were losing money? "Huge losses" is how George Gillett once put it. How much money did Gillett make when he sold the team? How about Paul Beeston's famous quote? "I can turn a $4 million profit into a $2 million loss and get every national accounting firm to agree with me." How about Alan Eagleson?
Now whether any, all, or none of those things are true is largely irrelevant. The players don't trust the owners. They don't trust their numbers (why would Fehr ask for them if they already had them all?), they don't trust the process. 57% is a meaningless number to them, as is 50%, as is 43%. Because it doesn't say what it is 57/50/43 percent of. The infamous HRR. 50% of HRR sounds like a good deal, but what if it doesn't include ticket sales, beer sales, playoff money, or TV contracts? Not so good, right? Extreme example, but you get the point. If they say "50%" as a player I would immediately want to know "of what?" As Bob Mackenzie said the owners want the players to take a smaller piece of a smaller pie. That's important, because without knowing how big the pie is the actual percentage is meaningless. How does the definition of hockey's "57% of HRR" compare to basketball's "50% of BRR?" The devil is in the details.
The players don't feel that they "deserve" 57%. They feel that they "deserve" a fair share, and that by their words and actions the owners can pay them more than what they are now offering. If you worked for a company that boasted about how great the company was doing, to the press and to it's shareholders, but then came back to you at your annual salary review and said "sorry, you need to take a pay cut because there is no money" wouldn't you be suspicious?