Air carrier Captain reported a discrepancy between the flight crew and ground personnel regarding the cancellation procedure of the NOTOC document.

Narrative

As we were preparing the aircraft for departure at the gate; we received an NOTOC ACARS printout to expect dangerous goods (DG). As we finished boarding I told the agent we could not close the boarding door since we had not received a NOTOC. The ground crew then connected to the interphone in the tug and said they did not board the DG and marked it refused. I said that was fine; but per our FOM (Flight Operations Manual) the NOTOC would need to be cancelled. This then generates an ACARS message that the NOTOC is cancelled and clears us to depart. I have received a NOTOC cancellation message before on a previous flight so I know it is possible. The ramp crew didn't know what to do. I contacted the Dispatcher and then the duty pilot. The duty pilot gave me the codes to relay to the ramp supervisor / crew chief to generate the NOTOC cancellation. We still were not receiving a NOTOC cancellation message. My Chief Pilot (CP) then called me to ask what was going on. I relayed the same information. The duty chief called me to say they could not get the system to generate the message even though load planning and cargo all confirmed the DG was marked not received and not boarded. But I was advised by the duty chief I could not depart unless the message was received or an FOM waiver was received from ZZZ1. After an almost 90min delay my CP called me and said as long as I have a NOTOC that is marked in handwriting by the crew chief that the DG was not boarded; I was legal to depart. I made sure to ask him again since the duty pilot said I could not depart; but he told me the regulations allowed the NOTOC to be altered in handwriting by the crew chief to say not boarded. I received this NOTOC; entered the DG number in acars and received an acknowledgment of the NOTOC being received and we departed. The load close out also indicated no DG was boarded.I found this situation incredibly confusing as we have been told we cannot depart without an NOTOC cancellation message via ACARS one we are notified of a NOTOC DG shipment on our flight. I was told by the duty chief I could not depart without it or without a waiver. As my CP is my direct manager; I took his message that the handwritten alteration to the NOTOC was legal. We need clearer defined messaging on what to do in a situation where the crew chief has coded the DG as not boarded and no NOTOC cancellation message is received. Suggestions: A clearer process for what to do when an NOTOC cancellation message is not received and DG was not boarded. I was receiving conflicting information from the duty chief and my CP.