Claiming that it shouldn't tax government, though, is quite incorrect since the income tax does so No they don't. Show me where. The fairtax will be 'generating' some 15% of revenues by the government taxing government. There is nothing like that under the current system. A completely fradulant proposal, which is why the tax panel correctly altered the fairtax in their analysis.
Government taxes itself now by paying employees more that they would need to do if they (the employees) were not paying income tax; thereby taxing itself. The government could have exempted themselves from paying their own income tax - but they did not. The same thing applies to all government suppliers who pay THEIR employees more due to the income tax. The same applies to state/local government government employees as well.
Claiming that the government should not "tax itself" is both dishonest and incorrect since the income tax does not and all of the various flat tax proposals do not untax themselves either. You are merely ignorant of the facts, apparently.