If I remember correctly all of the people that were pulled out of the water were naked. Subsequent reports stated that they believed that all the passengers were already dead prior to takeoff. It was a sympathy ploy by the Iranians against the Americans.
The track supervisor on the Vincennes, who I knew and served with in the early 90's, had the Iranian Airbus "hooked" and the F-14 on the runway ball-tabbed. (Makes sense if you are Navy or Air Force). His displays showed IFF info for the F-14 and track information for the Airbus. He got confused during a tense situation. He ended up reporting the Airbus descending when it was climbing which resulted in a shootdown. It was a horrible mistake.
I taught NTDS at Damneck, VA and stood watch in CIC as CIC watch officer for 6 years on three ships. There is no doubt in my mind about how and why this happened. What you have posted is not true.