The causation is correct. In countries with socialized healthcare, promoting healthy lifestyle is a cost cutting measure. So the government does it a lot, through various public campaigns and annoying laws like banning free drink refills or 300% taxes on tobacco. Usually it doesn't work, but occassionally it does, pushing the entire society toward slightly better health. Done consistently over 70 years, it naturally leads to a much more health-conscious culture, almost entirely due to government intervention alone.