Basically you're setting the expectation that RPGs are "about" storytelling, which when we get to the secondary (in terms of time) split (between storygames and other games), the default expectation is that "storygames" are the right answer.
My point is that it adds little, if any information, and the expectations that it creates are not well-grounded in reality. It confuses more than it clarifies.
This is an excellent example. My point is that the clarity of your explanation is not diminished *one iota* by removing the term "collaborative storytelling" and replacing it with just about any other term (such as, perhaps, game).