The coverup is about the fact that the U.S. was there at all.
That’s an excellent point.
Another factor that I can’t believe people miss is that 0vomit admin officials keep repeating that there would not have been enough time to send a rescue party. How could they have known in advance how much time there would be? During an attack and/or hostage situation, you have no way of knowing when it will end. (Unless perhaps you planned it yourself.)