“The FAA controls airspace, not the DOD.”
In a regulatory sense that’s correct. In plain English, maybe less so. If somehow the US military could detect a fleet of 50 Chinese bombers flying into US air space, FAA would be irrelevant, any any “control” would be done by DoD. Again, assuming the bombers could be detected and that DOD has any capability of defending against bombers.
Control would still be maintained by the FAA. If there was a national threat, would the FAA shut down all commercial and private air traffic like they did during 9/11? Absolutely. Would the military have free reign of the skies at that point? Absolutely. But air traffic control is the domain of the FAA, not the military.