I've yet to meet a good mathematician who didn't know more about probability and statistics than 90% of the folks who call themselves statisticians. Math is math.
This myth that math geeks can't tell you anything useful is rather irritating. Sure some of them speak very abstractly, and they might use a technique that you don't understand to draw their conclusion, by they can also save you a lot of time by identifying a fools errand early on. Proper grounding in maths not simply an academic exercise.
Perhaps if one has a doctrate in model theory and has never strayed outside of the abstract algebra/group theory realm, they might not be qualified to speak on statistical problems. However, my experience has been that this is almost never the case. The mathematics people I've known have been, for the most part, extremely well versed in various forms of analysis, algebra, probability and, yes, statistics. You might be surprised how a lot of the deep mathematical concepts tie into statistical methods. There's more to it than performing t-tests.
Comments like yours are more or less exactly what I was speaking about. What makes you think that somebody with an advanced mathematics degree wouldn't know about statistics? Because it's not in the title? Go kick down the door of your local university math department and spring some statistics problems on them. You'll probably come out with the answers.
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.
This myth that math geeks can't tell you anything useful is rather irritating. Sure some of them speak very abstractly, and they might use a technique that you don't understand to draw their conclusion, by they can also save you a lot of time by identifying a fools errand early on. Proper grounding in maths not simply an academic exercise.