This is the beginning of a series of misunderstandings that represent very real possibilities of how such an event would have played out. The underlying cause of this, and the following, misunderstanding, is that the people doubted that there could be a prophet. They would have felt that the easiest explanation was more likely to be believed than the one that pointed to a true prophet of God.
Because the murder had taken place in secret, and recently, the first people on the scene were those who had heard of it from Nephi. Then, when others were made aware, they found people with the recently murdered Chief Judge. The easiest explanation of how they were first on the scene was that they had been the murderers. It wasn’t true, but it was a logical first assumption.