Mr. Nuttel is in the country for rest due to his nervous condition. He is a very sensitive man who is easily agitated. Vera, Mrs. Sappleton's niece, has told him a very convincing story that is reinforced, unwittingly, by Mrs. Sappleton when she joins them in the living room. Nuttel attributes everything that she says:
"I hope you don't mind the open window," said Mrs. Sappleton briskly; "my husband and brothers will be home directly from shooting, and they always come in this way. They've been out for snipe in the marshes today, so they'll make a fine mess over my poor carpets. So like you menfolk, isn't it?" (Saki)
Once Mrs. Sappleton refers to the return of her husband and brothers, Nuttel becomes terrified, he is piecing together what Vera told him with what Mrs. Sappleton has said and then when he sees them coming toward the house, he thinks that he is seeing a ghostly image. The specter is just too much for his already rattled nerves, so he bolts for the door.
"To Framton it was all purely horrible. He made a desperate but only partially successful effort to turn the talk on to a less ghastly topic, he was conscious that his hostess was giving him only a fragment of her attention, and her eyes were constantly straying past him to the open window and the lawn beyond. It was certainly an unfortunate coincidence that he should have paid his visit on this tragic anniversary." (Saki)
Keep in mind that Nuttel does not know these people, they are acquaintances, he is there through a letter of introduction from his sister. He has no knowledge of the family or that the husband and brothers are not dead. So he is easily fooled by Vera who uses him to entertain herself. Saki tells us that Vera is very good at telling a good tale. Nuttel is obviously very naive about the mischief that bored young ladies can get into. He is a victim of Vera's boredom, she has played a prank on him, he does not stay around long enough to realize it was a joke.