Coincidental does not mean that the components must be false or that the statement is carelessly made. It means that the present exclusion does not follow from the very meanings of the components.
Suppose a room has a rule that only one of two machines may operate today. Under that rule they cannot run together, although simultaneous operation is not logically contradictory in their natures.
The distinction is one of grounds: conceptual incompatibility in the oppositional form and a contingent arrangement in the coincidental form.