Without going back I can't say the exact misunderstanding here, but his wife would most certainly be covered by the NHS if she was legally resident in Britain. I saw no suggestion in his post that she wasn't eligible for NHS care.
I think some people have misconstrued the story a bit. His wife was found collapsed in a public place. Concerned people called the emergency services. She might have been having a stroke, or a heart attack, after all. When the ambulance arrived, it was established that she was drunk and incapable. So what is the ambulance crew supposed to do?
If she'd been completely out of it, they'd have had no option but to take her to hospital, one more A&E admission to clutter up the system and consume staff time and resources there. However, she wasn't. She was compos mentis enough to take care of herself if she was in a safe place, that is home. The ambulance crew couldn't just leave her where they found her. They'd much rather not take her to hospital where the staff have better things to do than sober up a woman who's simply had too much to drink. So they took her home.
And no, that's not "billable". It's part of what the ambulance service is funded to do. It's not all blue-light dashes to hospital with barely-breathing RTA victims. Sometimes it's dealing with low-level concerns that turn out not to be anything too worrying. But they deal with it anyway.
And as an aside, for something as trivial as this, nobody would care if the "patient" was eligible for NHS care or not. If the victim turned out to be a foreign holidaymaker, so what? It's not worth stressing about. Job done.
Rolfe.