Earlier quoted context omitted.
In fairness it's not really the finance department and the ceo, it's the ceo and the board locking horns. And the ceo and the board decided to shutdown the whole company until they get their little tiff ironed out. (Which, yeah, was a pretty dumb idea. But the ceo and the board are kind of known for having dumb ideas.)
No, it really is the finance department. Boards vote on the CEO and serve as his advisors and that is certainly not the correct metaphor. More importantly, Congress sets the budget through the House and Senate budget committees, which then draft and pass appropriations bills. This is the point in the process where we are stuck. The President is saying "bring me budget bills that have the things I want and I won't vet…
The US Treasury Department is most analogous to the finance department of most corporations. Which, incidentally, is also shutdown right now because the board and the ceo told them to close. (Just as an additional point of fact, the finance department of many organizations does not set departmental budgets. That's not how it works. One of the reasons they exist is to, "finance", projects. Which could involve the use of any number of financial vehicles.)