Don't you mean causality not implying statistical dependence, which is what these examples have been showing?

That's right, sorry.

I had gotten the impression that you thought causal systems where things are related to derivatives/integrals introduce a case where this happens and it's not due to "cancellations" but something else. From my point of view, correlation is not a very interesting measure -- it's a holdover from simple parametric statistical models that gets applied far beyond its actual capability.

People misuse simple regression models in the same way. For example, if you use linear causal regressions, direct effects are just regression coefficients. But as soon as you start using interaction terms, this stops being true (but people still try to use coefficients in these cases...)

Yes, the Harvard address still works.