I understand you motivation to help your buddies. But, another way to look at it is this. You are making the dispatcher look good. In my building, that's all the incentive needed to not help or ask anyone for help. I don't know how your co-workers feel about your dispatcher or center team, but all you are doing is make them look good.
Let me add, the dispatcher is the one who got Jer fired for 'threatening' his poor behind with some of his outrageous add/cuts. No one at my center has forgotten that.