Even in your ideal experimental scenario, the laws of probability state that before the 10,000,000,000th such study is completed, we will see a case where the findings turn out to be incorrect.

We learn by experience, and we build weightings, and both our gut reactions and careful conclusions are simply the ones which win the confidence ratings. Logic may be an exception by virtue of it's mathematical nature, but any facts involved are not, and we fall back on judgement calls most of the time even when we think we're being logical.