When the incident happened I worked with a woman who had served in the Navy at sea. Her opinion was that if the they had accidentally shot down an airliner during a training/practice exercise, hundreds of people on the ship would know about it and it would be impossible to keep them all from talking. Is there anyone from that ship who is on record saying "yeah, we shot down that plane?"
How many rank and file military personnel would be present for a capabilities test of a classified, state-of-the-art missile system? That's not exactly the same as a training exercise.
Her point was that the accident wouldn't be knowledge that could be kept confined to the bridge/CIC and soon everyone on board would know about it.