I wasn't particuarly speaking from an American perspective. I don't think the German federal budget would pay for an entirely new Landesstraße, or a Landes- anything, or the Japanese national budget for a kenritsu- anything. If the federal/national budget pays for it it's going to be a Bundes- /kokuritsu thing, even if some of the same types of things can belong to either level. Sure, some infrastructure projects will be done by pooling funding from multiple levels, but but I don't think the combination of being explicitly a lower level responsibility, being mostly or entirely funded at the top level and being operated entirely by the lower level is something that generally happens.
What he says...
The city I live in has an entire list of projects by quantity of outside funding that would be required for them to go ahead. Generally they look to local, provincial, and federal levels each provide 1/3 for major infrastructure projects, including major roads, transit, and so on.
In the case of a starbase or berth, it's likely that the local government or fleet has a project on the books but would not approve the project unless it received a fair proportion of outside funding. That's not to say that it would be paid for entirely by Council-level funds, but 1/3 agency, 1/3 member, 1/3 Council is not out of the question? Or even 1/2 member 1/2 Council? But these projects would not even make it past the drawing board without a funding agreement from the federal level.
Plus there is always the possibility of less straightforward deals like "we will lower your contribution to starfleet for x-years so that you can use the resources to build y" or the various deals between the various nations/factions themselves.