I mean, really?
If they do, doesn't that sound a bit odd?
If I pay federal income tax to pay for the salary of someone who works for the federal gov't, and then they have to turn around and pay the same tax, aren't then the feds just getting the money twice?
Vehicle registration goes to the federal government. So, vehicles owned by the federal government don't have to pay to register their vehicles every year like citizens. This is why they are exempt. Vehicles like police and fire, you'll see something on their license plate that says so... either a little e, or even the word exempt. Why have one federal agency pay another federal agency when all the money doesn't really go anywhere?
But, it's a little different with federal income tax. If the feds tax me, and my money goes to pay a salary for a fed worker, and then they have to pay fed tax as well, then the federal government is getting the money twice. I pay it once, then it comes out of someone else's check to be spent again. Now the government can say it has $20 instead of $10!
Of course, that's only if federal workers do have to pay a federal income tax. You don't really think the government would really do that, do you?