Hm, that was the whole point of my argument I believe. That this is an inherent left-leaning position, regardless of who is subscribing to it; possibly because in the discussion on how to handle such healthcare, it defends the social and idealistic dimension ("left") rather than the self-responsible and pessimistic perspective ("right"). Now we can argue about political relativism and that no position is inherently and objectively "left" or "right" and it only depends on who articulates that position - and as you might have guessed this is an idea that I am slightly opposed to. Of course we can start with the Overton window and shifting beliefs and the possibility than in a century from now on, universal healthcare might be considered, for whatever reason, a hardcore right-wing extremist position.
That's an American perspective. The right, in Europe, support universal healthcare (because they own the companies that provide the services and receive the tax money). It's been this way for a very long time.
Therefore, characterising Europe as left wing on this issue is a mistake.
I believe the position you're starting from is already biased by the notion that only a left/right directionality can exist and that other degrees of freedom are not allowed in political systems. Of course this is why I think first past the post the the R/D split in the US is so bad.