As a hiring manager, I'm given a number and that's what I get to hire someone with. If someone asks for more, I can usually try to accommodate, but if you want 100K and I can only give you 80K, then it comes down to whether you want the job or not.
As for rewarding your work... equity can certainly come into play, but if the principle is that I have to pay you what other people are making, then perhaps I just can't hire you to begin with. Some people would say that maybe I should not hire you if I can't pay you the same as someone else. I don't know if I agree, but I can see that argument. Still, I'm out a worker that I could really use to unburden everyone else on the team.
If you are willing to work for 80K, I am happy to give you bigger merit raises than your peers if you worked extra hard, but if you walk in the door unhappy with your base salary, should I cut into the bonus pool of others just so you can get a massive raise to make your salary equal to theirs? Didn't they deserve their raise too? Or do they deserve less simply because their base number is higher than yours?
Of course, there are policies like equity raises that some businesses have which ensure that people do get on that sort of footing, but that's often a separate pool and not all places can afford it.
What I don't think is that you should consider what someone else makes to be a reflection on what the company thinks of *you*. If you're capable, you may start lower, but I'd probably be happy to see you become a manager or advanced individual contributor where that other guy will never get higher than he is today. You'll start at 80K, but you'll someday get to 150K whereas the other guy will never see the other side of 110. Alternately, you could be selected for more training opportunities or given more interesting work. All of that turns into more money too, either at that work place or at another place you move to later.
The problem is that it is very hard to do what is fair because the conditions in which "fair" are measured in can change. If we're making hundreds of millions of dollars, then its hard to justify giving you low pay, but if we're not, then I can't afford to give you the same higher pay that would be fair when we were doing well. Fairness is a very subjective concept unless you very strictly define what you are talking about.