The man explaining it about the ‘tops up’ to the altitude means something to how the plane reacts if that goes into the zone (52,000 he said later to correct his earlier number) which causes a freezing that would have iced the plane....my understanding? is like a funnel effect. Not that the plane went up that high, but that it was affected by it flying THROUGH the storm.
The top altitude is a measure of the power of the thunderstorm — the higher, the more-intense, with higher winds in and near the storm.
It's true that if an airliner flies just above moisture it could still pick up icing, that could even flame out an engine. GE (designed the CFM-56 engine, common on airliners) put out a bulletin on it after multiple incidents of airliners experiencing "unexplained" flameouts on oceanic routes. Ice builds up in the engine core until eventually the engine malfunctions, more often when the power is reduced (such as starting a descent) but also in cruise at steady power settings.
Here's an article about it in the WSJ:
http://www.wsj.com/articles/SB120753185285993925
Just out of curiosity and pure ignorance, why would the pilot request a climb to 38,000 if the recommendation is not to fly over?
For reference:
Flying Techniques to Remember
Publications from the FAA and USAF give us aviators numerous tips and techniques to help with that occasional encounter with a thunderstorm. Some of them are important enough to repeat again.
* Don’t try to fly over thunderstorms. They can grow rapidly through your altitude, producing severe turbulence.
* Don’t fly under the anvil where hail damage and lightning can occur.
* Don’t fly into virga where turbulence is likely.
* Avoid all thunderstorms by 203 or more since lightning and hail have been known to extend that far from the clouds.
* Weather warnings are for thunderstorms defined as “severe.” These storms produce 3/4-inch hail, tornadoes, or 50-knot wind gusts. There’s a lot of damage that can occur in thunderstorms that are not flagged by warnings or a SIGMET (significant meteorological report).
* If you have to penetrate:
Go straight. Don’t turn around.
Avoid the altitudes with temperatures of plus/minus 8 degrees Celsius.
Don’t chase altitude. Hold your attitude and watch airspeed.
Use all anti-icing equipment.