Hi,
I ll give some indication of the correct answer so please feel free to supress after answering.
You ask which cross validation not to choice for a set a data containing patients status coming from 10 hospitals and to predict if a subject has a disease or not.
Since I suppose you were talking about a particular disease I considered that the  classes were unbalanced and we had to prefer stratified cross validation and not use the others.
But in the solution you say we have to consider more the fact  patients are coming from 10 different hospitals.
Is grouping  really more important than unbalanced classes?
When I look your exemple in the lesson, grouping had a very weak impact on the prediction.
Why not consider the hospitals as parameters among others and use them to predict the illness of the patients if really grouping is so important in that case?
Thank in advance for your answers.
      
    
 Both are important if you want to be sure to get a good estimate of the performance of the model.