No no, the involvement in healthcare isn't just insurance.
It's US (and any other) companies being given contracts to run hospitals and clinics and any other services.
That's the whole point of the Health and Social Care Act 2012. Any willing provider. Private profit-makers welcome. "NHS" reduced to a brandname.
This was all made explicit in 2012. The legislation has been passed, and the privatisation is now being rolled out bit by bit.