My experience of VHI, is they didn't care, and the hospitals would always try to bill your insurance, even when you were in as a public patient. I had this argument so often with hospital's, I have to assume its deliberate policy. I experienced this before everyone had insurance. I think the hospitals try to bill the most expensive route. VHI didn't seem to care anyway. For example they'd send people out for scans, taxi with nurse etc, even when there was one site.
In one situation we had, came in as public, due to delays, meant extended stay in hospital, only space was in private, so they charged the lot as private. Variations of the same, from hospitals and consultants. Sometimes an appeal to the main consultant helped. Usually it was a wall of bureaucracy and I got nowhere.