Yes, Piggy's statement about fear being rooted in people and Simon's remark about the beast being within the boys themselves both reflect a crucial theme in "Lord of the Flies": the inherent darkness and savagery within human nature.
Piggy's comment highlights the idea that the true danger on the island is not an external beast, but rather the potential for cruelty, violence, and irrationality that exists within the boys. This fear of people—specifically their capacity for savagery—underscores the psychological and social breakdown that occurs as civilization slips away in the absence of societal structures.
Simon's statement complements Piggy's by suggesting that the "beast" is not an external force but rather symbolizes the inner darkness and primal instincts that emerge when the boys are removed from the constraints of society. This notion aligns with the novel's exploration of the theme of the loss of innocence and the idea that the greatest threat comes from within, rather than from any external monster.
Together, these comments emphasize the central conflict between civilization and savagery, illustrating how the boys' descent into barbarism is not just a response to their environment but a manifestation of their inner fears and moral conflicts. Both Piggy and Simon articulate the idea that the true evil is not an outside entity, but rather the potential for chaos and brutality that lies within every individual. This speaks to the broader commentary on human nature that Golding explores throughout the novel.