Another issue is the requirement that doctors adhere to "standard of care" regardless of cost. If they don't, they are subject to malpractice lawsuits.

Elsewhere, quality of a good or service is traded against cost. But in medicine, there's a cost ratchet as ever more expensive and marginally more performant treatments are introduced.

This is another example of a requirement that both PE owned and non PE owned hospitals, presumably, followed.e (I would hope neither of them were ignoring standards of care in the treatment of patients.) Yet the metrics are substandard at only the PE owned hospitals. So you would need to outline how this requirement unduly burdened the PE owned hospital relative to the non PE owned hospital for it to be the cause of the discrepancy.

There may be such a reason, but you haven't outlined it in your post.