I think I have to disagree with the "old wive's tale" part, at least as a minor quibble if not as a major get-down-and-get-dirty argument.
It is an old Latin phrase, something like corpore sano, mens sano so it certainly has a history. And one can argue that without a healthy body, your mind probably isn't doing well either. But they do not go hand in hand. It is possible to have a very healthy body and a very unhealthy mind. And vice versa. For healthy minds in sick bodies, look no farther than the late Stephen Hawking. For healthy bodies with sick minds, look at any of the many serial killers whose exploits have made headlines.
On the other hand, I will have to agree that if you NORMALLY have a healthy mind but then become sick, your attitude might change very much for the worse. I know when I was having liver issues, I was not a happy camper and I won't swear that my thoughts weren't colored by my condition. As my liver returned to normal under treatment (and removal of the things that were messing with me, chemically speaking), my attitudes got better as well. So I would agree that there is SOME linkage. Just not hard-and-fast linkage.