There are two pieces to the final revelation of the guilt of the brother. The first is Nephi’s prediction that blood will be found on the edges of his garment. Perhaps had the brother not already become nervous that someone knew, he might have created a plausible story about it being animal blood. At that time, no one would have been able to tell. However, the brother is not thinking clearly because it is so obvious that someone knows. Eventually he confesses.
This confession is the essential second part of this episode. Without the confession there might be some doubt, but the confession makes the case final. Nephi’s prediction will be accomplished in full, down the confession. It is this confession that will absolutely clear Nephi of any charges, and simultaneously strengthen his position as one who knows the future.