Kuwaiti F-18 Apparently Shot Down the Three Strike Eagles

As the story notes, this coheres better with some of the other evidence: e.g.:

That the Eagles were hit at all

That they seem to have been hit in the tail(s)

That all crewmen survived.

If the Hornet used Sidewinders, the Es might not have been locked up, or might not have realized it. If they were locked, they might not have thought it was that serious. Sidewinders fired from behind are more likely to hit the tail. And they have relatively small warheads. (Older Patriots have fragmentation warheads, IIRC; newer ones are hit-to-kill; but in either case, they're going to make a much bigger mess of things they hit than a Sidewinder.)