Years ago, Ford experienced the same sort of thing with Mazda. When they took their Pinto drive train to Japan, and the Japanese 'copied exact' the transmission had much better reliability numbers..... simply didn't break as often.
Much research was done. Same design, same materials, same processes.... yet the parts and the assemblies worked better and lasted longer without failure.
It all came down to better quality control. Tolerances were nailed dead center, instead of 'acceptable between +/- some number'. Much less trouble with 'tolerance stacking' as a result.
If Skoda is using the same suppliers and getting the same parts as the parent company, it would be an interesting observation on the quality of the workers involved. You don't hear anyone in the west talking about the Yugo, or any other Eastern bloc products with much enthusiasm.