Vera is described as a
very self-possessed young lady of fifteen
at the very start of the story, when she has just met Framton Nuttel. Right from the start, Saki throws a hint that these two characters are entirely different, with Vera having an upper-hand with her "self-possession", that is, her ability to exert control over her actions. This is indicated when the purpose of Nuttel's visit is revealed: he is there, at the country house of people whom he does not even know personally, in search of a nerve cure.
Throughout the story, Vera decides to pull a subtle but powerful prank on Nuttel. She invents a story involving her aunt's house, particularly the open window in the living room. While Vera tells the story about a fake hunting accident involving her aunt's husband and brothers, more things are revealed about her.
She is dramatic, a good actress to her aunt, and, also in the words of the author, she is able to come up with a story last minute.
Romance at short notice was her speciality.
Nuttel is too nervous for his own good. He does not even know how to appear approachable in the least. He is also too transparent, letting himself "in the open" about his mental illness and rendering himself vulnerable to people like Vera.
The doctors agree in ordering me complete rest, an absence of mental excitement, and avoidance of anything in the nature of violent physical exercise...
Vera and Nuttel have very little in common, with the exception of their acquaintance with Nuttel's sister, and perhaps even their social status. There would be no way for someone of a lesser station to seek neither refuge nor hospitality from someone whom they do not even know, unless they are social equals. Judging by the hospitality of Ms. Sappleton, and the fact that Nuttel had made her acquaintance years back, we could argue there being a possibility that the two families are equals in this aspect.