The current official report says nothing about trying to fire her rifle. I don't know when the report was written, but I haven't see an amended report. The current report was released July 7. 
When you are a soldier, privacy isn't an issue. The U.S. government has a responsibility to capture indcidents on the battlefield accurately. There are teams of military personnel that are charged with deciphering what happened on the battlefield and this certainly (maybe most especially) extends to the rescue of a soldier. The film provided as precise a record of the rescue as possible..
Also, you said that her back was broken at the wreck, but Private Lynch admits that she tried to fire her M-16 but it jammed. If she did try to fight with a broken back, wouldn't that be, at least, valiant?
Is it Rambo? No, but it would certainly explain why the initial reports had her fighting valiantly. One, because it is what a soldier does and, two, she did try to fight, but her weapon jammed.
The current official report says nothing about trying to fire her rifle. I don't know when the report was written, but I haven't see an amended report. The current report was released July 7.