It depends on where you live, but a lot of large US cities have their own fueling stations. That way, the city can buy fuel by the tanker load and avoid gas taxes.
It’s both. Tax exempt paperwork is annoying, and one of the best ways to minimize it is to minimize the number of purchases that you make. Buy in bulk when you can, because one large purchase is less likely to have an error (or at least, more likely to be noticed) than a hundred small purchases.
“Like-for-like.” I work in state government. Time ago we needed to get some video equipment so had to contract with a vendor to acquire it. They literally just bought it from B&H and sold it back to us.
In my rural county the cops, school busses and basically all the public service vehicles like ambulances and plows fill up at the farmer's coop, where farmers get cheap gas for their tractors. I have heard that this is not technically legal, because that has is specifically for tractors and has some kind of special price because of that, but I don't know if that's true or not. I know you're not allowed to fill up your regular car there, but some of the farmer's and cops do.
I think this is usually specifically for diesel fuel. Certain places have diesel fuel with red dye in it that is tax exempt. Any fuel you buy from a standard gas station has a good amount of tax baked into the price and it's earmarked to go towards road and infrastructure repair. The thought process is, if you're not using said vehicle on the road, you shouldn't have to pay this tax.
So, they dye it red, sell it only at special places, and you get fined pretty heavily if you're found using it in street vehicles. Typically it's truckers that do it because most American cars (including cop cars) are not diesel. And I've never heard of this setup for regular gas.
I've lived all over, moved a lot, and have never seen a set up like here before, either. But, I've also not paid super close attention to farmer's co-ops before moving here and getting chickens and ducks and doing small scale farming/big ass gardening. Lol. I assume they also sell diesel like you're talking about. Maybe they just got a deal with the county and I'm/other people here are confusing that for the red diesel thing?
Maybe. But in that case they would be exempt at a normal pump as well. Gas station by my house accept tax exempt transactions for the cemetery my family maintains.