Why wouldn't Nehemiah go into the temple, even to save his life?

Shemaiah's plan was, "Let us meet together in God’s house, within the temple, and let’s shut the doors of the temple; for they will come to kill you" (6:10). Nehemiah gives two answers as questions: "Should a man like me flee?" and "Who is there that, being such as I, would go into the temple to save his life?" (6:11). Then he says what the plan was for: "He was hired so that I would be afraid, do so, and sin" (6:13). So the chapter counts doing what Shemaiah said as sin, and it names fear as the way to it. It doesn't say which law he had in mind. The book calls him "the governor" (8:9), never a priest, and the law had given the priests their charge "for everything of the altar, and for that within the veil" and said, "The stranger who comes near shall be put to death" (Numbers 18:7). The chapter doesn't cite that verse, and this study doesn't say it was his reason. What the chapter does say is that he would not flee, and "I will not go in" (6:11).