Well, I'd agree that you probably can't go from correlation to causation without introducing assumptions - but there are situations where you can try to make assumptions.

For example, in the social sciences it's common to look for "instrument variables" which are random and can't be affected by anything else. If you can find these types of variables then you can pretend that you're looking at the results from an experiment.

There are also methods like discontinuity analysis, which argue that if your system is discontinuously effected by a variable, but the causes will effect the variable in a continuous way, then you can look at changes around that specific point as being causal.