That scenario seems wildly improbable. First, the existence of the large U.S. airbase at Diego Garcia isn't remotely secret. As for an accidental shoot-down of an airliner before any visual identification or confirmation, I suppose it could happen but it goes against every policy and procedure the U.S. is known to follow. If an unidentified aircraft approached an airbase, they would scramble an intercept for visual identification - especially in peace-time - in the middle of the Indian Ocean far from any active conflict zone.

In the insanely improbable event that the intercept accidentally shot down the unidentified aircraft before realizing it was a civilian airliner, then it would have been pilot error for not following rules of engagement or, possibly, a flight controller or flight commander error. There's zero reason for the U.S. government to turn an individual mistake into a huge incident by trying to cover it up. Also, there are many examples of the U.S. military making such mistakes and NOT trying to cover it up.