I think that this is best handled with some good guidelines for the DM, and then a lot of DM judgment. Explain to the DM that the group's standing within the organization and the kingdom will affect what they can requisition. Give some examples (if their boss loves them but the head of the organization barely knows they exist, they can ask for and get X type of thing in Y amount of time. If they need it quicker, that's going to be harder to get - their boss can't pull as many strings - and so on). This goes for requisitioning both goods and services.
As a long-term drone in a real bureaucracy (business), it's interesting if you have relationships with higher ups and can buck the system when you need to. I can get (a few) well-placed execs to listen to me based on previous interactions -- like telling one exec what another is likely to think about an idea and how to deal with his likely painpoints, that sort of thing gets you cred. But, the thing is, anyone with power tends to be very busy. So sometimes, you can't get to them when you need them, and it takes longer to cut through the BS they could otherwise hand wave away, regardless of your rep score with the org.
I'd model that with GURPS rules on Patrons. As in patron with X power, but you can access their help only Y times per year, with variable wait of 0 seconds (assuming cell phones exist) to 1 week, randomly simulating that they might be on an international trip or whatever. And you typically have to pay for it with the Disad of Duty to them -- they'll need your help sometimes too, or you wouldn't have the Patron. "Alright, McBain, I see your point. We'll send the Mounted Patrol to check out the parking lots at the Big Game after all, since you might be right about that terrorist threat to blow up a tailgating party, even though Captain McStupid said it was stadium security's problem and he wasn't going to authorize overtime." Later scene: "Hey, McBain, Chief Bossyboss here. I need you to babysit a Federal star witness for a mob trial. It's just for the weekend, and they shouldn't know he's here, so it shouldn't be any trouble at all. (DM smirks.) Can you pick her up at the airport in a half hour? Thanks."
Less powerful patrons (like the manager of a detective squad) should be cheaper to get more frequent/quicker access to, with a Duty to them too, but less likely to be Quest-level in it's nature, and more likely to be frequent: 'Hey Boss, I need some uniforms to get statements from potential witnesses." "No problem, McBain, I'll send a squad car to canvass the block." And the Duty side: "Hey McBain, fill out your TPS reports by Tuesday, or they'll be hell to pay with Captain McStupid. Yeah, yeah, I know about the Federal witness case, just get it done. Shouldn't take more than d6 hours away from the actual adventure, err, case."
Or you could just do the rep point thing.

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