You don't know what "allowables" are, apparently. Look at your medical bill. Actually read the whole thing. You'll see several numbers. Likes so:
Date of Service: 12/25
Procedure: Labor and delivery, in manger
Charges: $1750
Allowable: $1000
Insurance paid: $800
Patient responsibility: $200
What's happening above is Dr Angel charged $1750 for his services, supplies, labor, etc. But your insurance (Annunication Health Care) has set the allowable to $1000: that's the maximum price Dr Angel, per his agreement with Annunciation, is allowed to charge for that particular service. He can try to charge more, but Annunciation will not pay more-- and neither will its patients. Dr Angel agreed to that. It's contractual. If he wishes to change that he'll have to wait until the next contract negotiation--and if he demands too much Annunciation may decide not to participate with Dr Angel-- they'll send their patients to someone else.
So, the maximum charge is now $1000. Dr Angel eats that $750, whether it was real costs or inflated. Now Annunication's contract with its patient, you, comes into play. You have pretty good coverage: 80% for maternity. So Annunciation pays 80% of that allowable $1000, or $800. The remaining $200 is on you, the patient.
The point is, the insurors definitely do NOT pay whatever the providers may charge, they very much DO "tell Ford and Chevy they're charging too much". It's a contract. These things are negotiated and agreed upon and both providers and insurors spend a great deal of time and energy and research into fighting on each and every line item in the contracts. That's why companies change insurances, that's why insurors stop coverage with particular providers, and vice versa. Why do you think some doctors and hospitals don't take X brand insurance? Why do you think most insurors have "networks" of providers they send their customers to? It's all in contracts. And the insurors absolutely and definitely do "set the rates". The providers agree, or don't do business with them.
eta: it's also why in some practices I've worked in one of the most highly-paid employees was the person in charge of insurance contract negotiations. Particularly the drugs. Getting an insuror to pay an extra percent of a particular cancer drug can spell tens of millions of bucks right there by itself.