I read the entire article, and I saw no indication that they studied differences within the same hospital. Therefore, the entire study is worthless.
My take on this is that the authors were too eager to trot out sophisticated data analysis techniques, and did not focus where they should have, the study design.
I would like to better understand your point. I don't know much about the technicalities you are alluding to.
If each facility is analyzed in isolation, and assuming that the total amount of data collected from that is the same as the way they did it, won't you get the same results?
Typing that, it comes to me that your suggestion could allow for more possible conclusions (and options for improvements, if truly needed). One possible conclusion might be that there are differences between urban / suburban, for example. Perhaps blacks in a suburban hospital get the same meds as whites. Perhaps whites in an urban hospital get less.
Is this what you are driving at?
I need to go back and reread how they handled Asians and Hispanics.