Huge companies like SAP or Microsoft or Oracle will do this, even though they may also hire a traditional branded health insurer to "manage" this large-bank-account health plan (i.e. give out cards, negotiate with hospitals, etc.). But the bank account (brokerage account, really) remains in control of the corporation, and the traditional plan premiums are not paid to the health insurance company named on the card. Fees for managing the plan are paid separately. Doctors and hospitals get paid from the corporation's account. This is what the parent means when they say that the corporation has visibility into employees' healthcare usage.
And while these companies do have access to detailed claim data in theory, in practice access to this data is typically heavily limited a small number of HR or finance employees who are responsible for healthcare accounting and financial management and the data presented is typically restricted to a large claim report within a monthly/quarterly reporting period.
"The Privacy Rule allows covered providers and health plans to disclose protected health information to these “business associates” if the providers or plans obtain satisfactory assurances that the business associate will use the information only for the purposes for which it was engaged by the covered entity, will safeguard the information from misuse, and will help the covered entity comply with some of the covered entity’s duties under the Privacy Rule."
https://www.hhs.gov/hipaa/for-professionals/privacy/guidance...
>>"Covered entities may disclose protected health information to an entity in its role as a business associate only to help the covered entity carry out its health care functions – not for the business associate’s independent use or purposes, except as needed for the proper management and administration of the business associate."
BAA's keep the chain of HIPAA in place but just because a BAA is in place does not allow for violation of privacy.