What you’ve described is the self-insurance model for large companies. That doesn’t conflict with any of my earlier comments. Companies can decide whether they want to administer it internally or use a consultant.

You seem to believe that just because a company uses a consultant that no one in HR or Finance or management would be privy to viewing your claims history via the consultant? Not sure what would lead you to believe that. Just because your company is outsourcing the task doesn’t mean it is shielded from the data.