You'd be very wrong. There are hundreds (thousands? tens of thousands?) classified missions going on all the time involving large amount of people. And aside for the exceedingly rare whistleblower, all of them are kept secret for decades or more until they get declassified (sometimes never).
(Not trying to give any credibility to the previous comment, just commenting on how effectively governments keep classified secrets.)
Not many of them involve murdering an entire planeload of civilians.
You of course don't know that, not having access to compartmentalized top secret material.
If you did, you couldn't post here (or anywhere) about it.
The US has vast intelligence and military resources, but resources can't create operational miracles. Disappearing a civilian airplane and keeping it disappeared would be such a miracle.
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.
Including shooting down an airliner. No coverup.
Carrier group is even less likely to shoot down airliner. In middle of ocean or crowded area like South China Sea, carrier group probably doesn't have its defenses on alert. It has fighters that can intercept and visually identify aircraft. In the middle of ocean, there is plenty of time to react. There isn't the hair trigger in middle of war zone that led to Iran Air Flight 655.
A related suggestion to be aware of is that the plane was shot down by the US or US-friendly forces, as several of the flight simulations were reportedly the pilot landing at Diego Garcia, a relatively secret US air base in the Indian Ocean. The theory continues that the US purposely got the search parties to focus on a different search area first while they cleaned up the debris