Statisticians are claiming too much for their discipline, much as economists were claiming too much for theirs prior to the crisis of 2007-2008.
They claim too much, because:
(i) All statistics are founded on, and bounded by, human knowledge and judgement; human fallibility regulates what we see and what we do not see, what we know and what we do not know, what we imagine to be relevant and what we imagine to be irrelevant.
(ii) Statistics can only describe the past, often with the aim of predicting the future. The past is a treacherous guide to the future, even if we happen to be right about the past, which we never are, entirely.
(iii) Statistical descriptions of the material world do not capture the political and moral dimensions of whatever they describe — and there are always political and moral dimensions, even in the tossing of a coin. (Is it your coin? Is somebody for forcing you to toss it? Is anything contingent on the outcome of the toss?)