From your summary health appears to mean 'not sick.' If you can clarify what health is rather than what it is not you might be closer to an answer on whether exercise and health are related. Spoiler: yes.

There's the level of physical activity of most of my ancestors, and there's the level of physical activity of my ancestors since the clerical explosion (1800s-present). The former group has a longer track record of success than the later, and for that reason alone I'm guessing they for sure got it right (with a provisional 'not all bad' grade for the inactivity of today). Regular moderate activity of some kind with bursts of heavy activity leads to physical strength and physical grace more often than not.