Before I defend that statement - are you arguing that poor health does not cause dementia, that poor health does not disincline one to dance, that the types of poor health which cause these two things are different, or that the effect size somewhere is small enough that most of the observed correlation must be explained by something else?
(The claim of causation, by the way, was not in the study; it was added by Richard Powers.)
Frequent dancing causes a 76% reduction in the risk of dementia. The benefit seems to be from freestyle social dancing, though I don't think that part is as well-verified. The benefit seems to be from making large numbers of quick decisions.
I wonder if playing jazz has similar good effects.
For something a little geekier, Shiva Nata, a system of keeping the mind fresh by doing more and more complex movements. The author of the blog is a silly person, but the system seems to be for real.
Edited to correct html which was entered in the text field instead of the html field. It wouldn't surprise me if having to deal with electronics and computers tends to prevent dementia, considering the number of fiddly and changing details one has to deal with. Or is fun required?