Unfortunately, we have no reliable information from the primary actor on the American side: the National Security Agency.
What information we do have from the NSA consists of two parts:
The problem is that the NSA story about the mission is a lie; the story includes a great little bit of fiction about how we found out that the planes were being flown by Commie Russians just before the attack, as we monitored the radio signals between the airborne Badgers and their Cairo military airfield.
There's only one problem: the aircraft had bugged out for Alexandria on Day One of the war and did not fly at all for the duration of the conflict.
If the one part is a lie, the odds that the second part is a lie increase tremendously.
Turned out to be a climbing Airbus instead.
Good summary...
Definitely SOMEONE is lying...and very probably more than one someone. The big question is why...and there isn't enough evidence available to US to come to a definite conclusion at this point -although some very highly-placed Americans who were/are in a position to have inside info HAVE come to some definite conclusions on this -conclusions at odds with the official story. Without them, it would be just one more conspiracy theory.
The devil(s) would be found in the details, but -once again- too many people on top have no interest in those details coming into the light. All the more reason to keep digging.