Hmmm. Thought it (the basic, unadulterated quote) was based on marketing during Prohibition?
“Over the years apples were developed more for their sweetness and for eating out of hand rather than for cider. This was partly in response to early prohibition efforts. The old saying, “An apple a day keeps the doctor away” was part of a late nineteenth century marketing ploy to keep the apple in favor with the public as a healthy food versus its use as an alcoholic beverage.”
http://harrison.ext.wvu.edu/r/download/50127

That's right : the aiming part is attributed to Churchill (and the origins of the expression dates back to late 19th century, according to your source).