the methods rely on a number of assumptions that you can't test (like independance).
You can test independence. There is a ton of frequentist literature on hypothesis testing, and Bayesian methods too, of course. Did you mean something else?
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.
My favorite is that people get credit for updating based on evidence.
The more common reaction is for people to get criticized (by themselves and others) for not having known the truth sooner.