Poirot’s comment that he slept as if he had been drugged may, in fact, be true. Since Poirot’s reputation precedes him, a smart murderer would specifically try to keep Poirot from observing important events. There is precedent in other Christie stories, like
Murder on the Orient Express, where the murderer interacts directly with Poirot. The Allertons are not major suspects in the case, though comparing the testimony of various passengers will be important in the coming chapters.