Peter would not have stood over a body he already knew was dead, but instead chased after James Bennett who was armed and dangerous.
When Neal's father came into his apartment and saw Sara he asked if she was Kate, then Alex. He obviously knew nothing about Kate (who was dead) or Alex.
Peter watched Neal talking to Pratt and the disgusting gesture he made after he had forced Hughes' retirement. As an experienced FBI agent, he would have been left in no doubt that his replacement was going to be a plant and would therefore not have meekly given up the existence of the box.