It is probably more than half the story. Health span is strongly correlated to life span, although not completely. The median "health span gap" is about 10 years, and has widened by roughly one year over the past 20 years. However, this is probably just due to an aging population and not necessarily from any factors you can control fully.
I wouldn't be surprised if "health span" (although defining it is difficult) exactly mirrors the inheritability pattern of mortality.
> The median "health span gap" is about 10 years
It depends on the definition, if you're even just 20kg overweight you're living a wildly different life than you'd have if you were fit, you're closing so many doors by default and making a bunch of things much harder than they should be, But you're still considered "healthy" here