You seem confused.
As someone who has worked directly with medical (dental) insurance, the billing hospital/doctor almost definitely sent the bill to the insurance company first, were denied the claim, and then sent it to the couple afterwards.
You seem to think the hospital told them they weren't covered, but that isn't what happened. At least not in this article. They thought it was covered and dealt with until returning to the UK, where the insurer told them they weren't covered.