I'm not sure how the various NFA laws and regulations interact exactly when it comes to the government. Basically if you are a federal agency as far as I know there is absolutely no NFA regulations that apply at all. Which is why you keep getting situations where ATF and other agencies can't account for all of their machine guns. They can't even tell you how many they're supposed to have with 100% certainty. Some agencies tracked them as a special inventory item, others as far as the paperwork is concerned it was the same as a cell phone or a laptop computer. They can have direct government contracts with manufacturers or importers and can buy from any FFL without filling out a 4473 if they present a purchase order on agency letterhead.
Now State and lower agencies, they don't pay any tax but they also have to do the registration just like everybody else except the feds. Most laws have the 'except for us" exception at the end so I have no idea other than filling out a form what the language of the actual law does or does not exempt them from as regards to NFA requirements. Even if the law says they have to get permission to take out of state and all that sort of thing, it could be argued as a 10th amendment states rights issue. Especially if it doesn't and this is just ATF adding their own regulations.
Such is the current case with the Hughes amendment. It's simply states that the machine gun ban does not apply to the states and their agencies. ATF however says they will only transfer law enforcement appropriate firearms. M16, mp5, MP7, the odd Aug or Uzi perhaps. But if you put in a transfer request for something like a world War I Vickers expect to be denied. Again states rights, who is the Federal government agency to tell a state they can only acquire arms that are approved by the federal government? Especially when they made the regulation up out of whole cloth without any explicit restriction in the law itself.
If we can get some state attorney generals on board, there might be some interesting court cases coming up in the next few years...