It was precisely because he knew, understood, and accepted his good friend's character that he refused to believe that his good friend would betray him and allow the commoners in Lizhou to suffer because of something that could be used against him.
His good friend must have been a stopgap measure.
He felt that it was better to let the people of a state suffer for a while so that Qiu Pusheng's gang can be brought to justice, ending the suffering once and for all.
Although the choice was very difficult, when the choice was placed in front of him and he had to choose a path, he made this choice.
His good friend had always known what he was doing.
The Prime Minister's wife's words also made him understand why his good friend was so determined to die and didn't tell him the evidence he had collected and what he had done. Presumably, he must have felt that no matter what decision he made, he had still caused the people of a province to suffer.