Comment by pierrebai

Is this trying to be too clever? If the correlation is weaker than the random noise of the data, then it is equivalent to not being correlated.

Otherwise, we'd get conclusions like the color of your car influencing your risk of lung cancer or some such nonsense. With enough data, you could see a weak correlation of red car to cancer, but it would still be insignificant. That's what the null-hypothesis is for: to put a treshold under which we can just ignore whatever weak correlation seems to be there.