I do not think it does overlook that research: those papers generally assume that once those things are controlled for, the remaining variation is as good as ra

I do not think it does overlook that research: those papers generally assume that once those things are controlled for, the remaining variation is as good as random and thus we indeed recover the causal effect of X on Y. Many papers are probably _wrong_ on this, but they still use "causation" in the first sense and not in the second sense.