I've found that a lot of fans seem to think that players will/should take discounts to play for a particular team. They reason that if a particular player likes playing in a particular place, he would certainly be willing to take less money to stay. Let's call this the 'why Ryan Smyth was upset about his contract negotiations' argument.
Think of it this way: You work at a widget factory, assembling widgets. You assemble 24 widgets an hour, a rather remarkable pace. A friend of yours works at the widget factory across the street; he's a slow worker, and although he puts in the same effort as you, he can only manage 18 widgets an hour. Despite this, your friend makes 24 dollars an hour while you only make 18. At the end of the year, your boss calls you into his office to discuss a raise. He offers you 20 dollars an hour for your 24 widget an hour pace. Sure you're happy at your current job; everyone is nice to you and you really like your co-workers, but you can make a lot more money at the other factory, where it's likely that everyone will be nice to you, and you will like your co-workers.
Would you accept 20 dollars an hour, or would you go across the street and see if you can get a job at the competing widget factory?
People get caught up in the fact that hockey players make millions rather than thousands of dollars a year. Although this is true, it's important to realize that while the criteria for evaluation has changed - hockey performance rather than widget assembly - players still 'think' in the same way we do about these things.
Wouldn't you be insulted if your boss offered you a raise that was less than your under productive buddy makes across the street? I know I would.
Clearly there are extenuating circumstances such as 'winning the cup'. However, let's say for the sake of clarity that the team (factory) competing for your services has an equal chance of 'winning the cup'. In this case, would you you be insulted by the lowball offer? Remember, your boss knows exactly how many widgets your friend produces across the street, and exactly what he is paid to do it.