After 24 years, at least a few swabbies would be smart enough to realize they'd been lied to.
WERE they lied to? They Navy scoured the water and dredged the bottom for pieces. How do you know what they picked up? How would anyone?
Why WOULD the Navy shoot down an airliner if it wasn't an absolute emergency? IF they shot it down, that is. And if it was an emergency, and if the reason for that emergency was a political catastrophe for national security, do you really think someone would talk, and thereby put the country at risk? How low do you want to go with your estimates of the characters of military men and women?