I got slightly side-tracked when you said "we mean" and I wanted to clarify if you meant "the people having this discussion in this thread".

But I actually made the point:

    Supplementary insurance is conceptually different, by definition, from comprehensive private health insurance which provides alternative coverage for what is already covered within the public healthcare system.

Maybe I could have added for more clarity:

  And that's what the person you replied to means with "very few people have private health care in Europe, at least in the UK".