Indeed. They call this "effect modification" in epi. I guess in some sense, this is just another guise for the curse of dimensionality in the context of determining causal effects. Lots of covariates might be relevant for why [X] helps you, but trials aren't very large, and simple regression models people use probably aren't right very often. So it's hard to establish if E[Y | do(x), C] - E[Y | do(placebo), C] is appreciably different from 0 for a sufficiently multidimensional C.

edit: In case it is not clear, p(A | do(B=b), C) is defined to be p(A, C | do(B=b)) / p(C | do(B=b)) (under appropriate assumptions that preclude dividing by zero). This is one of the reasons I don't like the do(.) notation so much. In counterfactual notation, we can make a distinction about whether C is under the interventional regime or not, that is in general p(A(b) | C(b)) is not equal to p(A(b) | C) (but it is for any pretreatment covariate C, because then p(C | do(B=b)) = p(C(b)) = p(C). That is, the future cannot affect the past.