I have not followed this story to any degree. However, a news story I just read was so full of errors, I wanted to comment. These are technical comments for those interested.
There is no such thing as a "thunderstorm higher than 50,000 feet" (above sea level) that does not show up on ground-based weather radar, provided the storm is within range of the radar and the radar is properly calibrated. This nonsense about a "phantom" storm is just that, nonsense. However, weather radars are few and far between in that part of the world.
Second, there is no such thing as a thunderstorm, as described above, that does not show up on airborne weather radar, provided the radar is properly operated and calibrated. However, there are quite a few pilots who do not properly use airborne radar. They leave the radar's antenna tilt fixed (say, -2°) and never touch it. That can keep the radar's signal above the storm and the storm is never seen by the crew. That is different than saying the storm was not detectable by the radar.
With regard to air traffic control (ground-based) radar (ATC), a "primary" radar target -- in spite of what the name "primary" might suggest -- is not the "main" signal. A primary is simply the radar's signal bounding off an aircraft's skin. If the aircraft is equipped with a transponder, the ATC radar will show the name of the flight (i.e., "United Flight 802"), its altitude, etc. A "primary" signal is simply the aircraft's location and nothing else.
Hope all of this is helpful.
AccuWeather is covering the meteorological aspects of this story, here.
ADDITION: A pitot tube is not an air speed "indicator," it senses wind speed.