Only if the budget was reasonable in the first place. All too often they "budget" far more money than is possible and then celebrate the cuts.

This is two different things, not helped by the multiple meanings of the word budget. If the organization makes the budget (i.e. a spending plan) without confirming the funds (or knowing them through, say, a long term understanding), and don't get what they seek, of course that's not somebody else "cutting" their budget. That's just a budget you made up not being agreed to.

But this is more about having an expectation of funding at a certain level from whatever source, and knowing that that will be your "budget" (now meaning a spending _limit_), then having that amount come down. You now have a smaller limit.