I've been pretty bothered by the vitriol with which this paper is being received, and wanted to make a couple of points about how I read evidence like this: https://twitter.com/fperrywilson/status/1360944814271979523

In that case it's probably defensible to not use something like a multilevel model here because there may be no information at the cluster level.
The point is that clinicians at a research hospital probably know what cluster randomization is, so if they didn't analyze their data with those methods, that may have been a choice based on the knowledge of their experiment rather than some undergrad level blunder.
This isn't to say just believe everyone, but maybe write them a polite email to ask why they made certain decisions, or offer help to make different decisions.

For example, on pubpeer one of the authors is equating "RCT" with a placebo controlled trial. This is probably a language issue and not that she doesn't know the difference.
https://pubpeer.com/publications/DAF3DFA9C4DE6D1B7047E91B1766F0#11
https://pubpeer.com/publications/DAF3DFA9C4DE6D1B7047E91B1766F0#11
Before saying "you are obviously contradicting something you wrote many times in the paper" try publishing something in your second language and seeing how clear and nuanced it is.

So I would just contemplate how you'll feel if these results turn out to be valid. If you're a skeptic who's spent a lot of time convincing people to not adopt this safe practice which may save their life, how will you feel if you're wrong?