While I think this has changed over time, initially I think some statisticians were suspicious of techniques coming out of computer science, e.g. SVMs. And still, machine learning is a rather niche field of statistics that requires a fluency in CS that many statisticians don't have (or need). Check out this discussion.
Of course there are some statisticians who are also good CS people (think Trevor Hastie and Rob Tibshirani). And a lot of stats people have great domain knowledge in their areas. But I think "data science" is supposed to be the combination of stats, CS, practical programming ability (e.g., cleaning and manipulating large datasets, which is definitely not part of traditional CS or stats education), ability to communicate results effectively, maybe throw in some visualization, knowledge of how to query databases, and domain knowledge to interpret what data mean. Also, some types of data (e.g. text with the aim of NLP) are pretty infrequently touched upon in stats education.
That said, I get the sense that a lot of places looking for "data scientists" are actually just looking for business intelligence people.