Perhaps your experience has been different from mine, maybe because I'm based in the UK - I know that US education tends to be more generalised. Among my friends with or pursuing postgraduate degrees in pure mathematical disciplines, none have any particular knowledge of stats above the undergraduate level. As a master's student, I wouldn't imagine I count for much - but what I know about statistics could be written on the back of an envelope. It's something I've been meaning to remedy for a while now. It's possible that tenured professors have a wider breadth of knowledge than the average PhD - and I admit that I wouldn't know if that were the case.

As for the depth of statistics as a field, and its reliance on other disciplines - I agree entirely. I think pure mathematicians are far more likely to be ignorant of statistics than statistical mathematicians are of, for example, analysis.