Yes, they do indeed pay taxes,at all levels.
Been there, done that, got the tax returns.
You have paper work, to show that you went through the motions just like the rest of us, but in reality, you didn’t pay anything into the treasury, unless you have investments outside of your government salary that earned money that you paid taxes on...........
Money paid to you from government coffers, local, state or federal, came from someone else who paid taxes on their earnings. Any taxes you ‘paid’ on those earnings simply wasn’t given to you, and stayed in the treasury, but did not increase it.
If every person worked for the government, then there would be no one to pay their taxes into the treasury from which your salary is drawn.
You fill out your tax forms and possibly even get a ‘refund’ on your taxes, but that money simply comes from a person who doesn’t work for the government who actually pays money into the treasury, or the government prints it to make up the difference.................