I agree with gurugeorge response and see Popper the same way.

That said, I do think that although Pearl's work is great, the key word is "in principle" - the methods rely on a number of assumptions that you can't test (like independance) and he also says that the experiment is the only guaranteed way to establish causation (in his talk the art and science of cause and effect). I also may be wrong, as this talk was given in 1996, he might have changed his mind.

Moreover, your "trust your intuitions sometimes" is misleading: it is still not simply trusting your intuitions, it is trusting them only in the cases where there is data suggesting that intuition gives better results in similar cases. It has data behind it - the intuition is not taken for granted.

As Popper wrote, sensory data comes through organs that aren't 'perfect' sensers. Our brain is also not a 'perfect' thinker. We know all that thanks to our knowledge of evolution - and that's the starting point of Popper. Popper didn't have Kahnemans' or Pearl works, but he still encouraged critical thinking of hypotheses while not treating intuitions as given (only as hypotheses, and only if they were falsifiable), and falsification is still the basis of science at this moment.