When noontime came and it was time for Red to distribute rations to all the occupants of the underground shelter of Rogue Shelter, he had no choice but to pass the job to Graham since he had already planned to leave. Red would've had done it himself to garner the appreciation of the people but he figured that he should just delegate the job to Graham. Because ultimately, he was leaving the shelter anyways, although perfectly knowing that it might be a one way trip to death and not just a trip to ask his dad something about his past.
As for Graham, he had been Red's assistant even before he was assigned to missions and a Unit. That's why he knew that there was probably a reason why he had to give the distribution task to him. For all the years he had served Red, he knew that Red was the kindest person in the world. He was not one to make excuses and skip a job so important.