Hello
Why is written that the features are not centered for the best hyperparameters with ”‘columntransformer__num-preprocessor__with_mean’: True" ?
Good catch, it seems that we did not fix the random state and most probably there is a combination with no centring that is almost as good as centring and interchange depending on this random change.
I will make sure that the example is reproducible.
I fixed the random_state in FIX make randomized search reproducible · INRIA/scikit-learn-mooc@5f10819 · GitHub
The discussion is aligned now with the results. @earm75 it shows that you can have several combinations close to each other and selecting the best mean test error is arbitrary 
One can synchronize the notebook by clicking on File → Revert to original