I have to admit I am not entirely sure that I understand your question. What you seem to be talking about is how does Saki make this story so effective in terms of his design of the short story. This is of course a darkly humorous tale where a poor, sick man is exploited by a ferociously intelligent and quick young lady. To me, this story celebrates the power of storytelling to deceive and to mislead - it is highly ironic that the story ends with yet another tale that conveniently explains away the strange behaviour of Mr. Nuttel.
Of course, what is absolutely key to the success of this story is the fact that we only find out the "truth" about Vera at the end of the tale when she weaves this second tale to explain Mr. Nuttel's swift exit. The last, brief line seems to sum up so much of Vera's character:
Romance at short notice was her speciality.
It is only at the end of the story that we realise how Framton Nuttel has been deceived and exploited for Vera's own amusement - and how she has just done the same to her family. Although we as readers have the benefit of discovering the truth at last, we, just like Framton Nuttel and Vera's family have been taken in by her convincing performance and her sheer verve at storytelling, and so, in a sense, the joke has been played on us as well. In this, I believe, lies the success of this great story.