So when a fighter jet is scrambled for one thing or another in U.S. airspace it first has to get permission from air traffic control? Odd . . . I never knew.
Technically, yes. But since an aircraft launched on an actual air defense mission has such a high priority in the air traffic system, the controllers are basically getting everybody out of his way.
Scrambling jets is one thing but they still coordinate with ATC. How would they know if they are going to collide with a civil aircraft other than onboard radar?
As far as other flights, such as training routes, yes, they do coordinate with the FAA and the FAA has the authority over them. I don’t know of any law that says the FAA controls US airspace but the military has supremacy.