There is a little bit more to the story.
The US was engaged in hostilities with Iran (the Tanker Wars) at the time. VINCENNES was involved in a running gun battle with IR patrol boats. And was expecting further action from the Iranians. The Airbus took off from a joint use (military/civil) airport and followed a standard comair profile. It was being monitored/tracked due to the origin point and the fact that it was going to overfly the cruiser. As standard procedure, the cruiser attempted to hail the Airbus on IAD (121.5) which was probably not being monitored on the airliner.
Now, as the Airbus continued to climb toward VINCENNES and the ship was still dealing with the patrol boats, people got sloppy in CIC. Internal comms/procedures...etc. Someone on the CIC tape called out 'he's descending!' No track number....nothing. Just that statement. And that statement combined with the track visually heading toward the cruiser and due to the close proximity, the CO ordered the engagement.
It was later determined that the track display readout on the Air Warfare operators screen had swapped to a US fighter jet that was descending to land on the CVN. In other words, he looked at the visual display of the Airbus while reading the speed and altitude information of a different contact that was 'hooked'. Had the CIC watchstanders followed proper procedure and used track numbers in their transmissions regarding contacts, they would have caught the error.
So, yes, as far as the internet is concerned, they 'mistook' an Airbus for an IR F-14, but as with most things, there is a bit more to the story.
Wouldn't that mean he confused it for a US F-14?