It wouldn't take very long for the relevant parties to know whether they accidentally shot a missile at a 737. For a mechanical issue, there would be much more uncertainty (although it's possible the pilot reported the issue to ATC).

And even then, "ATC, we have a catastrophic engine failure" from the pilots doesn't discount that the catastrophic engine failure was caused by a missile. The pilots don't magically get to know what caused the engine to blow up.