'Severe' turbulence is rare. It often leads to a situation where the aircraft cannot be controlled and has to descend.
There has been a fair bit of moderate turbulence across the Atlantic recently. The effect of turbulence can also be dramatically different between the front and back of the aircraft.
As for 'climbing or desending to get out of it' - often the aircraft cannot climb as it is at its maximum height. Descending, unless control difficulties are being experienced, takes a fair bit of organisation over the Atlantic due to the traffic control system. Often the turbulence extends from lower levels to higher and there is 'no escape' anyway.
As said, the passengers are repeatedly told to keep their belts fastened unless they need to move around the cabin. If the signs are on they should all be seated and strapped. If they are not I have little sympathy for them and they risk injuring fellow passengers. If they are strapped in they will be safe, not necessarily comfortable.
Aircraft are built and pilots trained to cope with turbulence.
As with all media I suspect the story anyway!