First of all, the study doesn't claim that the high-level bureaucrats don't want more funding, just that they want smaller increases than the general public. That fits in with the theory that bureaucrats want to expand their domains. However, I suspect that high-level bureaucrats have better incentives to be efficient than (a.) the public, or (b.) the politicians who actually create budgets. They are more likely to understand how much funding their group already has and more likely to be fired or criticized for inefficiency.
It's pretty widely known that polls usually reflect support for more public funding for everything except foreign aid and the arts. Economically, that makes sense. The public is not sensitive to the cost when it is just an abstract question (should x get more funding?) And of course the politicians who create budgets have little reason to be careful with money (they don't get to keep it if they don't spend it, so they might as well convert it into political capital with some group or another).
So that seems to paint a picture of a system where the public and politicians have an unlimited demand for spending because the marginal cost is near zero, and the bureaucrats get to expand their domains without being seen as unusually greedy or wasteful.
Jerry Pournelle's "Iron Law of Bureaucracy" implies that leaders of bureaucratic organizations will seek to maximize the power and influence of the organization at the expense of its stated goals - but is that true in the real world?
Julie Dolan of Macalester College examined surveys of government administrators and found that, surprisingly enough, high-ranking federal bureaucrats tended to prefer less government spending than the general public, even on issues that their own departments are responsible for.
Here is the abstract from her paper, "The budget-minimizing bureaucrat? Empirical evidence from the senior executive service" that was published in the journal Public Administration Review:
I was able to read the paper here for free, but I had to register first.
See also: The Case FOR Bureaucracy