Commutators and direction of current
When using it as a generator, the commutator isn't responsible for changing the direction of the current in the coil itself. The coil current changes direction just because that's how it physically works; the job of the commutator in this case is to 'undo' that direction change so that the output current stays in the same direction.

That said, don't feel bad. I would have picked c) as well; it's only your mentioning that a) is the correct answer that got me thinking enough to make this realization. It's a tricky question.