This is not a valid point against medical studies, because medical studies never attempt to prove causation. They are merely showing that event A preceeds event B with correlation of 0.51 or so. The human body is so complex that controlling for every variable is simply not possible. It's not just funding either. To control for every variable you'd need more test subjects than there are humans alive. Furthermore all medical double-blind studies do indeed only show correlation (nearly always very low correlation, a successful drug will have correlation coefficients of maybe .53 If you find a drug for almost any disease that correlates with curing any disease of .7 or .8, you can start a pharma company and it'll be worth billions).
Also while correlation does not imply causation, it does mean 1 of 3 things. Suppose A and B correlate. Let's take a flu medication and getting cured as an example.
1) A causes B (people who take the drug tend to get cured from the flue as a result)
2) B causes A (people who get sick, and heal by themselves tend to take the drug because they feel sick)
3) A and B are both caused by the same thing (can be many things, e.g. the medicine salesman has the flue)
There have been attempts to mathematically define causation as correlation with a time offset (the one that preceeds is the cause, the one coming after is the result). This has had only limited success. That of course does not stop nearly every study outside of the pure sciences from taking such time-delayed-correlations as proof of causation. Are you really suggesting throwing out 99%+ of science over that ?
( and 4. you made a mistake and while it looks like correlation, it's not. E.g. longterm correlations in chaotic variables, like taking the .999999999999999999 correlation between mathematical descriptions of planetary orbits and concluding those planets are actually in those orbits until something large happens [1]. Yes it goes for earth too. The orbit of the earth could alter to throw the earth into the sun, or out of the solar system and there would be little or no warning. There is also no need for "large" events to cause this. Planets' movements do not follow the central limit theorem and therefore cannot be predicted with 100% certainty. The huge problem is of course, that in the real world nearly every problem exhibits chaos, for obvious reasons, not just the stock market)
[1] http://en.wikipedia.org/wiki/Three-body_problem