I carefully caveated for a number of factors, actually, with "healthy": anyone recovering from an injury, ill, or otherwise excusably unable to be fit is inherently discluded from the group I'm saying should be able to run a mile. Likewise, pregnant mothers who have to be on bed rest. If you have to be on bed rest, you're clearly not healthy, and so on.
The average has absolutely nothing to do with the ideal or even the minimally acceptable standard. The average is simply a metric to represent the mid-grade of the current population, approximately. I would not want to be an American of average fitness; I imagine it would be equal to approximately no fitness. The average American woman is over twice my size. I would not find that an acceptable size to be, personally. And I don't think other people should simply because it so happens that it's the mean.
I don't think we are necessarily disagreeing. I will say I think culture and location are probably significant factors in what the average or minimum standard of health are. French women don't get fat, and so on.
I believe that humans are meant to run. It is that belief which drives my conviction that all healthy people should be able to run a mile non-stop, and my suspicion that if you cannot - hell I will be generous and even say you have a week or ten days in which to build up to an attempt - you are simply not healthy. This generally flies in the face of the Health at Any Size movement, which I don't usually go out of my way to disagree with - but obese, sedentary people (or obese people who are able to "walk long distances without being short of breath" - often populate the HAES movement, even using the above quote as a demonstration of health, when I consider it a requirement for life and not an acceptable baseline for health or fitness. I think being able to run a mile non-stop should be the bare minimum standard for anyone to claim they are fit or healthy. I don't even care what you weigh, to pull in your last point. If you are 250 pounds and can run a mile non-stop, I am willing to say you are healthy. But if you can't, I'm not. And god, if you're running a mile non-stop, at least you're trying. Being able to walk long distances is not trying.