Yes. I don't know if that's the primary factor that gives them their market power; it might be even simpler than that. But yes, they absolutely do.
Unless you're Kaiser, in which case you're the insurer and most of the providers, which is the whole idea behind Kaiser. But every other insurer --- and overwhelmingly, Americans aren't on Kaiser --- is beholden to providers. And of course, Kaiser competes with providers for service providers and vendors.
Then why isn’t everyone on Kaiser? Because they’re stupid?
Providers is also kind of vague. You show up at a hospital, does the nurse practitioner who does your intake set the price of your ER service? Who specifically sets the prices?
UnitedHealthcare operates in DC and all fifty states and has north of 26 million customers. Kaiser operates in eight states and DC and has around 12 million customers. It's safe to say plenty of folks use Kaiser when it's available.
The downside is that because Kaiser operates as an HMO, any specialists you need to see must be approved by your primary care physician (typically GP, ob-gyn, or uro). They have an abysmal record with mental health, and folks who need chronic non-routine care often struggle to get that care. If all you need are routine checkups, cheap prescriptions, routine immunizations, etc. they're quite competent.
Who specifically sets the prices?
Kaiser is a vertically integrated HMO. Like other HMOs, to get coverage (with a few exceptions) you need to see a provider within the (Kaiser) network. As a vertically integrated HMO the providers in the Kaiser network are all employed directly by Kaiser. So Kaiser sets the its own employee compensation.
It's worth noting that all insurance companies are required to emergency care at any provider as if it were in network. If a Kaiser member were to go to a non-Kaiser ER they would see the same cost as if they'd gone to a Kaiser ER. Whatever Kaiser pays to the out of network hospital/staff is almost certainly negotiated beforehand.
I acknowledge there are issues on the provider side, but it is disingenuous to say that providers set the prices alone. Payers introduce a ton of inefficiencies in billing and also remove money from the system, which negatively impacts care. They implicitly affect care patterns and pricing through denials.
HMOs, for all their problems, have many advantages as well, such as the aligned incentives you allude to.
So, I don't disagree that there are inefficiencies with private payers, but I do disagree that they're significant, or the reason US costs are so high, or that insurers deny so many services. You can see this for yourself with Medicare's admin overhead. Admin overhead is, roughly, the ratio of money spent by insurers to money insurers pay to providers. Medicare has "low" admin overhead --- but that's in large part because they serve the most demanding segment of the market. If Medicare covered 30 year olds, their admin overhead would mathematically be significantly higher: same money in, much less money out.
I agree with you about the efficiency of HMOs, but customers hate HMOs.
A useful Google search: "National Health Expenditures by Type of Expenditure and Program: Calendar Year 2022". It's a single spreadsheet, and it's really something. It covers insurers (public and private), providers (hospitals and outpatient), facilities, state health care programs, even dental, all on one sheet. The numbers are hard to get around.
Providers overbill. Insurers inappropriately deny coverage. This is pretty basic stuff. What would insurer overbilling even mean? You pay a fixed premium.
Your second link is literally Anthem passing provider fees (in violation of their contract, sure!) through to customers. The bills were from providers.
Fuck if I know what's going on between Medicare and UHC. It's a mess. Medicare Advantage is a hybrid Medicare/private system; once again, whatever fees were being passed to Medicare, they were coming from providers. Insurers can certainly inappropriately deny coverage, but they don't generally make de novo charges up. Charges come from providers.
Upcoding scandals, which literally appear to be what the UnitedHealth link you provided was about, were exactly what Anthem was trying to control for with its new announcement.
Unless you're Kaiser, in which case you're the insurer and most of the providers, which is the whole idea behind Kaiser. But every other insurer --- and overwhelmingly, Americans aren't on Kaiser --- is beholden to providers. And of course, Kaiser competes with providers for service providers and vendors.