Sounds sensible but is probably speculative bunk. Ronald Reagan was President -- certainly a mentally stimulating job -- and even after he left office I'd be surprised if he just sat around watching the tube.
What was striking in Reagan in his declining years, and I've noted in most people with the dementias, is the lack of head movement and the resulting atrophy of the neck muscles -- indicative of decreasing circulation to an area, in this case, the head, face and brain.
In people of older years in declining health, that seems to be the major marker. So it is that area that needs to be addressed in exercise over every other. The major beneficiary of exercise should be head and brain function -- over every other consideration. The heart is automatic (autonomic); the head (brain) are voluntary movements that don't just benefit because the heart is beating automatically.
Voluntary muscles direct the flow of blood and nervous impulses to an area. Simply being "mentally" active is not enough; there has to be actual, concurrent physical movement of the brain too. One of the great problems of medicine is this thinking that one thing in the body is not related to everything else in the body -- or that the physical and the mental are entirely different systems of operation.
The brain has to integrate "physical" exercise -- and the muscles have to integrate "mental" exercise as essential components of total health. The integrity of health is only as good as its weakest link. It is that fragmented, compartmentalized view of human functioning that is a large part of the problem in aging that they are helpless to address with that conventional view.