9/11. (No, no conspiracy) A question about military/civil communications

Just watched some "movies"/"documents" about 9/11. The military dispatched two F16 AFTER the first plane already hit.
They explain the delay by "civilian and military ATC do not 'speak' the same language" (?)
Fair enough, the phraseology may be different, but how would they not be able to communicate?
When I fly from Portimão to Lisboa, I am first with Faro, then with two costal military ATCs (I don't know where they are, but they certainly know where I AM!), then back to civil with Lisboa. Comms are smooth and chaps are nice. Aren't ALL the ATC able to pass-on infos from one to another?

I am USAF air traffic controller, have been since 2008. Saying it is difficult to track aircraft, “even when the transponder is on,” completely undermines what we do as controllers. If the aircraft’s transponder is on, we can very easily track the aircraft’s position, direction, speed, and altitude and vector interceptors simply and easily.

Now when the transponder is off(elimination of secondary target), yes it makes things more difficult but we can still track estimated altitude and observe speed variations off of the primary target. A 747 and a Cessna do not behave the same on a radar scope, we can tell the difference very easily with a few seconds of observation and the estimated altitude. Example: if the primary return has an estimated altitude of FL370 and is moving at a fast pace it is OBVIOUSLY not a Cessna, as a Cessna cannot fly at that altitude, nor at a high rate of speed.

Now for the PAVE PAWS(Not MAWS) system, it is used primarily to track SLBM’s and there are only a three located around the United States(Beale AFB, Clear AFS, and Cape Cod AFS); they are not something you will see in major cities, however, there are similar types of radar used for various other reasons. As far as I know, they have no aircraft tracking capability, though they would still obvious give off a primary return on their equipment.