Think the economic reality is that the days of a doctor hiring a couple employees and hanging their shingle are over. The capital requirements are too high and the counter parties too big for individuals to thrive anymore. PE is one of the ways to consolidate and get some economies of scale. Plus I think most doctors prefer doctoring to running a business.
But there's nothing to stop all the doctors in an area from forming a cooperative. That would also be private equity, but not in the sense described in the article.
The PE in the article is firms with other values than what traditional medical professionals have, and those values are conflicting.
There's some anti-trust complications with loose cooperatives negotiating as a collective. Fine line between collective bargaining power and price fixing.
Organizations more like employee owned businesses exist but those come with their own sets of problems.