I agree that, as a statement about current best or accepted practice, inferring causes from data needs to be done in a domain dependent manner. I have the hope and desire, however, that our mathematical methods can be greatly improved so that (a) they are better able to capture the sort of domain relevant information that humans use to judge when data can support causal inference and (b) they lie less when folks turn the crank.

I don't think this is a naive or far off hope, either -- I think you can get a lot of the way there by doing good old fashioned Bayesian inference starting from priors over Pearl-style graphical models.

Of course, this might not help your particular problem at all; I get the impression that in intracellular biology, almost everything can potentially affect everything else, which leads to weak priors which leads to the data rarely being able to tell you anything about causes. Still, that's better than your analysis telling you the wrong thing.