I wasn't very clear, and probably misleading. Although I'm not an expert, I have "read" Pearl's book a few years ago (Causality: Models, Reasoning, and Inference, it's available as a pdf) and it really seemed to me that some independence was hard to test, and sometimes was an assumption given the system. It's also true that I haven't read it deeper now that I have a bit more knowledge, and I lack time to do so.

If you have more hindsight about that, I would love to read it.