Admirable? What was admirable about burying a dead man? If anything, Archer could admit that his actions were despicable. He was abandoning Isobel's emotional needs, taking charge of the situation, and burying a young man's body in an unmarked grave without alerting the authorities or his family. When he returned to the building, Archer also planned on looting Trenton's apartment, as he wouldn't be using anything in it postmortem. No, Archer had no delusions - he was not being admirable. But he was taking control and making a decision, which was necessary.
"It's what has to be done," he said simply. Was he supposed to thank Cole for saying that he was admirable? He didn't want to. Cole was mistaken. Why would he thank the other man for being mistaken? Noting that the grave had sunk another foot into the ground, he stood, wiping his brow with his sleeve. "I'll relieve you," he said, taking a step forward and reaching out for the shovel.