Look at the flight times quoted for a trip from LA to London,
Outbound: c.10 hrs 20 mins
Return: c.11 hrs 20 mins
The distance is the same but the travel time is about an hour shorter. Aircraft cruise at very similar speeds (i.e. they don't fly any faster to get to the US) the world is rotating London to LA direction and hence it is rotating under the aircraft bringing the destination nearer to get to the UK while moving it away on the trip to the US.
Sounds like cobblers to me. Transatlantic time difference is more to do with head/tailwinds. The Earth imparts rotational inertia to an aircraft while it's on the ground, and that inertia doesn't suddenly vanish when it becomes airborne. The Earth doesn't "rotate under" a transatlantic flight any more than it rotates under a hovering Harrier.
I think.
