I am not sure about this visas explanation . In my company everybody, pilots and CC have C1/D visas only and we donīt always depart with the next available flight. We have layovers of several days due to different A/C types flown while there are daily flights, up to 6 on the same day to the same destination. And it was the same in the company I used to work before this one. Never had a problem whatsoever at immigration. Could be a matter of agreements between countries?