A DH is positive space. As long as you are at the gate 30 minutes prior they can’t deny you boarding. I have had them deny me boarding when we could not make 30 prior for different reasons. I just called crew scheduling and let them know that the next flight segment was uncovered or went to the hotel and picked up an extra days pay. On two occasions I actually had crew scheduling bring the aircraft back to the gate and put us on. One was a scheduled DH and the other amazingly was commuting to work as a non rev. The non rev one I was called at the last minute for a GS. Told them I might be able to make a 3pm flight but it was iffy. They asked me to try as they had no one else. Arrived at the gate at 2:50 with the last few passengers heading down the jetway. Agent refused to board me. I really didn’t want this trip anyway so called crew tracking to tell them I would not make the flight. The tracker said it’s 2:55 and the flight has not pushed. I explained the agent would not board me. He said don’t go anywhere your getting on that flight. Agent came back out of the jetway as the aircraft was pushing. Said he would roll me to the next flight in 3 hours. As he is talking I see the tug pulling the aircraft back into the gate and the agents phone rang. It was station ops reaming him a new one for not putting me on the flight and now they were going to take a delay. Fun watching him try and explain why he didn’t!