As this is an answer to the question, I post it as one: As far as I know there is still no conceptual explanation of this observation. We were looking at this situation for unitary reflection groups in Proposition 2.1 in our preprint arxiv.org/abs/1404.5522, tried to give an explanation and discussed possible approaches with David Bessis. However, this lack of understanding still seems to be the state of the art.
Christian Stump
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