Apologies! It was late and my proofreading became less rigorous.
I'll rewrite it:
"The they're-a-bunch-of-quacks story doesn't have to explain the Nimitz incident. The AAWSAP/AATIP group were given footage and reports of the incident, but the existence or nonexistence of the event is independent of what that group says."
By analogy:
People see a man in the distance stumbling through the woods covered in blood. They go to help, but can't find him. A hunting camera catches something moving through the trees around the same time the man was spotted. The police investigate, but it goes unresolved.
Years pass. A private detective appears in our story. This detective has unconventional views, such as believing that dogs can see dead people, vampires exist, Hitler is alive and imprisoned under the White House, etc. The detective has written about these subjects. In past unsolved murders, he has claimed Dracula was the murderer. Once, he tried to get a homeless man arrested after a stray dog led him from a grave to a back alley.
The private detective convinces the police chief, who already has some suspicion that vampires exist, of the danger posed by vampires. The police chief decides to fund the private detective, telling him to investigate the vampire angle.
Whatever the truth is regarding the blood-covered man, the police chief should have looked at the detective's wide range of bizarre beliefs, considered the severe deficit in judgement that those beliefs indicate, and not given him funds to investigate the case. Especially as it turns out he's using some of the funds to investigate all of his other wild beliefs, and even used funding to pay the costs of a group of Hitler-is-under-the-White-House believers.