I think it's more about being able to see things from the audience's perspective.
It's hard to write good documentation without being able to visualize:
- What they know
- What they don't know
- What they're probably trying to accomplish
Some of the best API documentation comes in the form of examples, which doesn't draw much on writing skills.
That said, explaining high-level concepts/theory does require writing skills, but it also requires the skills described above.
The skills to write good documentation approach something more resembling an English major than a programmer.