Similar to people thinking they have a policy from the processor rather than their employer, health providers are completely unaware that my employer pays the bills. If the providers don't get paid according to the contract, they'll go after the processor. The processor wants a buffer, insists on escrow or something.

As employees, people are seldom under the delusion that they work for, e.g., ADP. My last company paid me through a processor. My direct deposits showed as coming from the processor. To any bank, it looked as if I was employed by the processor, but the employees knew who the employer was. Should the employer suddenly cease to exist and owe employees anything, employees will go after the employer, not ADP.