Scheduling generally doesn't know the circumstances for the schedule adjustment unless they are told by the pilot or duty pilot. They just do their job to cover flying. This is why the duty pilot call is a requirement. BTW both pilots independently have evaluate there willingness to continue, just as with any other fitness for duty scenario. Regardless of the pressures to continue serious thought needs to given to the ability to duplicate the outcome on the very next flight. At a previous employer they would just shut you down, no questions and no decisions, just policy. It gives you time to reflect and document which is a big part of what happens next.