I'm not sure if this is a myth, but is it bad for a pianist to work out (e.g. lift weights)? I've heard that building strength this way will reduce fine muscle control.
This is a myth. An untrained person with large muscles will be just as clumsy as an untrained person with wimpy muscles. Fine motor control is a skill learned independent from the rest of the muscles in your body - if it were related, all brass players would have gi-normous lips and pianists would have gi-normous hands, and as well all know, this is simply not the case.
Physique only becomes a factor when a given body type will not allow a person to play an instrument with correct technique. For example, someone with a severe underbite who wants to learn to play clarinet. Other examples would be a person with fantastically large hands who is interested in oboe or a person with a weak jaw that wants to play tuba.
With respect to piano, it usually comes down to hand size - the larger the hands the easier it is to play. Certainly if you're of the muscular persuasion, piano will not hinder in the slightest as playing to the extremes of the instrument may be thought of like doing "flys."