I'm clueless about healthcare economics, but this sounds fishy to me. Why would insurers go along with that? In fact I would expect insurers to be in a much better position to bargain with a hospital than a private party. Actually it's if the hospital were billing the govt (not as motivated as a private party) where I would expect that overcharging to creep up and up.
Insurers can only spend 15% of premiums on admin spend (e.g. salaries, etc). That means if the CEO (and everyone else) wants more money, they need to pay more money to the hospitals, so their 15% cut grows.
Also, for beyond that, unspend premiums have to be refunded, which also cuts into the potential admin spend bucket, so it's best to always ensure your paying as much as possible in claims.
Plus, patients hate denied claims, because typically your forced to sign paperwork saying your responsible for anything insurance refuses to pay.
And with most health insurance spending being locked to employer benefits, the big market is the group market, which means your stuck with either getting your job's option(s), finding a new job, or not getting insurance basically.
In other words, you don't have a price choice as an individual in a group.