Part of the problem is that data science doesn't have nearly the same formalism in its definition that statistics does. What's the difference between BI's, Data Miners, Data Analysts, Data Scientists, etc? The tools used to arrive at conclusions (R vs. Python vs. SAS vs. Tableau/Excel/SPSS) doesn't seem like a good way of differentiating the roles.
A more useful discriminator would be the application of statistics (BI vs. Biostatistician, for instance), the depth and complexity of the statistical algorithms used, and whether the main use is stat inference or prediction (machine learning doesn't seem to focus on inference a whole lot, for example).
I agree wholeheartedly. It's not just data science, but all science that requires good statistics.
EDIT: IANADS, but data science seems tightly intertwined with statistics, to such a degree that I've had to double-check the difference multiple times. (Seems to be mostly terminology-based, tbh.)