These are two distinct issues.
The study you linked concerns whether the hospital is owned by a nonprofit or by a private equity group.
The question in this study is whether physicians work for their own practice or for the hospital directly, regardless of the ownership of the hospital.
This issue is much more linked than you think, because its a strategy to upcode to have external practice groups.
Your assertion runs counter to the original article, which says that acquiring external practice groups raises prices.