The contract does two jobs, and losing it loses both. When a provider joins a plan's network it agrees to a schedule of rates, and it agrees to accept the plan's payment plus your cost share as payment in full. Those are separable promises that happen to arrive together. The first is why your explanation of benefits shows an allowed amount far below the billed charge and why the difference is written off. The second is why nobody sends you a bill for that difference. A provider without a contract has made neither promise, so a plan that pays "something" out of network is doing one of those two jobs and not the other, and the missing one is the expensive half.
Network status belongs to the individual contract, not to the address. This is the most consequential misunderstanding in the area, and it is not obvious from anything a patient sees. A hospital's contract with a plan covers the hospital's own services. The physicians practicing there may be employees of the hospital, or of a separate group that contracts independently, or of nobody in particular, and each of those arrangements produces a separate answer to the network question. That is exactly the situation federal surprise-billing law was written to address for a defined set of specialties at in-network facilities. Outside that defined set, "the hospital is in network" tells you about the hospital.
One insurer can operate several networks. A plan sold under a familiar brand may use a narrow network built for that product, while another plan from the same insurer uses a broad one. A practice that says "we take that insurance" is usually answering about the insurer. The question that matters is whether it participates in the specific plan named on the card, which is why the plan's own directory or member line, rather than the front desk, is the place to get the answer.
Directories are wrong often enough that Congress legislated about it. The No Surprises Act added section 2799A-5 of the Public Health Service Act, codified at 42 U.S.C. 300gg-115, which requires plans to verify provider directory information, to maintain a database, and to respond to inquiries about network status. Subsection (b) supplies the consumer remedy, and it is precise. Where an item or service is furnished by a nonparticipating provider or facility, would have been covered had it been furnished by a participating one, and the enrollee received information through the plan's database, directory or response protocol stating that the provider was participating, the plan "shall not impose … a cost-sharing amount for such item or service so furnished that is greater than the cost-sharing amount that would apply … had such item or service been furnished by a participating provider", and "shall apply the deductible or out-of-pocket maximum, if any, that would apply if such services were furnished by a participating provider". Note what that does and does not do: it binds the plan's cost sharing and accumulators. It is not itself the prohibition on the provider billing you the difference, which is a separate part of the same Act with its own conditions. Keeping the printout or the reference number from the inquiry is what makes the protection usable.
What crossing the line changes, in the order it changes it. The plan applies a different deductible, usually one that has its own balance and has not been advanced by anything spent in network. It applies a higher cost-sharing percentage. It calculates that percentage against an amount it determined rather than one it negotiated. The spending is not required to count toward the annual limitation on cost sharing, so the ceiling that would otherwise end the year may not move. And the provider may bill the remainder. Each of those is covered in its own place on this site; the point here is that they arrive together and are caused by the same absent contract.