Everything Einstein said holds relative to the other things he stated. It's hardly a fact more like a gospel. All you have to do is create a setup where the disturbance doesn't equal the input energy. Sounds hard but it's awfully easy.
here we attached 2 spring scales to a wheel, lets pull both up to 10 kg.
Now we attach a 10 kg weight to our wheel and look at the measurement.
we get 10 kg of pull on the vertical spring scale and zero on the horizontal one.
we reattach the weight 90 degrees down the wheel. Again we have 10 kg of pull on both scales just like we started out.
and last but not least...
Now we read 10 gk on our horizontal spring scale and zero on our vertical one.
What is the point of all this you wonder. I understand - don't worry. :-) The point is that the energy content of the rotating wheel changes with an amplitude. Increasing the speed costs less energy while it spins slow decreasing the speed generates more energy while it's spinning fast. While the weight is at the top the rotational energy content held by the wheel is much lower. It will eventually stop spinning with the weight failing to reach the top where the speed is low. The small push it needs to go over the top can be extracted again at the bottom.
Just like you swing your legs on a swing while it moves the slowest.