Why does NASA have F/A-18s?
NASA uses them for pilot training and as chase planes for research aircraft.


  The two-seat F/A-18 support aircraft are normally used for photo or video chase. They are configured to transmit live video pictures from the air back to Dryden so engineers can visually monitor the mission as it is being flown. This feature greatly enhances flight safety.


There's an article from Armstrong Research Center with some more information, but that pretty much sums it up. 

NASA also currently operates (and has operated) many other military aircraft types, either as chase planes or as subjects of research projects. Some examples off the top of my head include F-15s, F-16s, and of course their ubiquitous B-52s.

You say "obviously they are battle ready", but they are not – NASA aircraft are unarmed, and the ones in the photo certainly are carrying no missiles. They may have been fighters in a previous life, but the weaponry has been stripped. "Escort" doesn't mean "fighter escort" in this case!