Local school districts have responsibility too
Having had both direct and indirect involvement with residential educational services provided through the Department of Education, I guess I'm confused by the apparent confusion. It is a fact that local district contract with facilities to provide residential educational services for their students. The Department of Education and sometimes other agencies share in the cost.
There seems to be an expectation that these services are fee-for-service (like a hospital) and that itemized bills are available. That's not true. Virtually all of these providers contract at a flat-fee rate for tuition (the educational component of the program) and room-and-board (everything else).
The contracts generally specify what services are included in each portion of the bill, in accordance with how the program is set up and operates. The contract might include medical monitoring, family therapy, individual and group therapy, and what-have-you, depending on the program. These services, however, are bundled into the overall rate, and not billed separately, with few exceptions.
Finding out "what you're getting for your money" is usually simply a matter of reading the contract (what you agree to pay for and what the provider agrees to supply) and cross-referencing this to the students record, to ensure the services are documented as they occur.
As the contractor, the local district has every right (and arguably the responsibility) to monitor this.
D. A. Lindemer, Ph.D.