LJ,
The Hawk was an attempted replacement for the phoenix and as such an A-A missile not a A-G or anti ship like an Excocet. The radar modes for the AWG-9 would at least have been operating in its natural environment. It would be a big ask of the Iranians to integrate a stand-off A-G weapon into the AWG-9. They had other platforms for this role.
Also the USS Vincennes should have known exactly what the radar return of an F-14 looked like as they would have engaged it many times in the past on excercises.
Which brings us back to the threat analysis. It took many leaps in logic to turn the radar return of an A-320 on a standard rising commercial flight profile into that of an F-14 (a dedicated A-A weapon) flying a ship attack profile (wrong speed/ climbing) with a stand-off weapon (which didn't exist on that platform) to be engaged BVR.
As far as I can see the only evidence they had was an IFF return. The Iranians may have a question to answer here as to how an A-320 could squak a military code.
We know that in the fog of war this happens but this one was avoidable.