This is the exact dilemma described in "High Output Management." Corporate organization is the art of deciding what to centralize and what to decentralize.
I think the business concept missing from Agile is investment/ROI and risk. Until budgeting processes are also Agile, everyone will be operating on the idea that "we paid $x to get 'y', and now you aren't giving us 'y'. What the hell?"
Agile works (when it works) because it treats software as a complex system that is best studied and modified through experimentation after accepting a high initial degree of uncertainty (which is slowly reduced through the creation of knowledge). The only comparable things in business terminology are investment and risk. Each iteration (I hate "sprint") needs to be treated as an investment with some risk percentage of failing completely. Until the money is handled that way, business people will keep expecting to get exactly what they think they're paying for, exactly when they feel they were promised they'd get it.