A father's innocent desire to care for a sick child can easily mask underlying dangers. Acting in complete good faith, David agrees to his son's request, entirely unaware of the dark plot taking shape within his household [ביאור שטיינזלץ]. Hoping to comfort Amnon, he sends Tamar to prepare the exact meal that was asked for [רלב״ג, ביאור שטיינזלץ].
However, the king's instructions to his daughter are limited. He tells Tamar only to cook the food, never commanding her to personally feed Amnon. David has no idea that Amnon specifically insists on eating directly from Tamar's hands. Had the king noticed this unusual and intimate demand, it would have immediately raised his suspicion, and he never would have sent her to him at all [מלבי״ם].