Actually
the 'chance' thing is not exactly word-for-word. From what I know,
physician back then had to learn a series of disciplines and in
order to diagnose what causes the illness. Birth chart is used to
see where and what's wrong with the body. Say, if plantary transit
is affecting the Kidney, there will be affliction in Libra or
something like that. It may seemed like taking a chance because
Libra to everyone is merely balancing scales, but objectively, if
you study Medical Astrology, it's more than just scales. And due to
Classic Science, as you can't quantify/measure it - there's no way
it can be proven by figures, so it is rejected.
Something like Acupuncture; it has been around for ages. Theory of
Acupuncture is relating to the flow of 'chi', disrupt it and your
body goes in a mess. Classic Science will try to explain the effect
of Acupuncture without the 'chi' theory because you can't put a
figure or quantify things like 'chi', so they will reject it. But
does it works? Yes it does. Result shown from people under
treatment benefiting from it. Is that chance? I say, people are
just making use of old wisdom passed from old science.
Afterall, back in the ancient, people generally don't suffer from
sickness like AIDS or Cancer. People were much healthier then. The
diets (preservatives and all kind of stuff they put into our food
now, were non-existence then. Soils were richer, food were greener,
fresher and purer), almost-free-of-pollution-environment, lifestyle
(people had work outdoors, therefore exercise, unlike now 8-5
desk-bound jobs, etc), mental health was so much better, etc.
As civilization moves on, of course, we need new knowledges to
combat new challenges. Older Science are generally less appealing,
so people don't study them anymore. However, the Science we have
now, is merely evolution of older Sciences, with improve theories,
school of thoughts and stuff. 
Cheers
