Zhou Shuren indeed had his suspicions, but he didn't expect the Emperor to disgust the Fifth Prince so much. Look at what the imperial edict says, implying he should provide round-the-clock care. The news he heard was that the fake Fifth Prince was bedridden, and such close daily contact hardly kept one's reputation clean.
Moreover, the true Fifth Prince wouldn't just sit and wait for death; he would surely find a way to return to the capital and reclaim his identity as soon as possible. The Emperor was forcing the Fifth Prince to reveal himself, and why did Zhou Shuren feel that the Fifth Prince would find some green upon his head when he appeared? And it would be public knowledge!
Zhou Shuren's gaze grew heavy; the Emperor truly showed no mercy to the Fifth Prince, and his and Zhulan's speculations were very likely true.