While there is definitely a theme comparing children's minds to adults' minds, it not usually framed as innocent "intelligence and ingenuity." The usual and textually supported interpretation of the theme is in terms of the enfant terrible, a description of children in Saki's stories, like Vera, who willfully devise means by which to torment or antagonize adults whom they seem to despise. Vera's supernatural fantasy would fall into the category of being devised to torment, specifically, to torment Framton Nuttel.
Saki is intentionally ambiguous (unspecific, allowing for multiple interpretations) as to Vera's motives and thoughts but (1) she knows of Framton's need for a rest cure, (2) deliberately acts the part of terrified girl when the three long "dead" men return, (3) and coolly invents another fantasy to explain Framton's sudden escape. Based on this, it is possible to interpret her motives as those of an enfant terrible who intentionally seeks to torment (out of boredom?). When we add to this the fact that she tells fantasies to her aunt and uncle, a strong case is built for attributing motives of antagonism toward adults.
Having said this, it is possible to see the more innocent theme of children with superior intelligence and ingenuity versus adults. Clearly Vera has a vivid imagination and the presence of mind to maintain her equilibrium and composer in the midst of inventing then reacting to a fantastic horror story of mental instability and ghosts or corpses returning from the dead. In addition to which, Vera calmly and coolly tells a second impromptu fantasy to give a likely and plausible explanation to her relatives for Framton's surprising departure. The theme of superior intelligence and ingenuity would focus on Mrs. Sappleton's and Framton's foolish and gullible behavior in believing and reacting to Vera's fantastic stories.
While on the one hand, Vera is "self-possessed" and tranquilly in command, on the other hand, the adults are nervous, excitable, credulous and generally inferior. While the adults can't think well enough to identify a hoax and lies (how often does Vera do this, actually?), Vera thinks well enough to use present circumstances and adult's ignorance of particulars to invent impromptu stories that are borne out by subsequent events and behaviors. This illustrates that children with superior minds are superior even to adults indicating that while adults may learn more information, skills and accumulate experience, a superior quality of mind is innate, expressed even in childhood, and an inferior quality of mind follows an individual even into adulthood.
"I expect it was the spaniel," said [Vera] calmly; "he told me he had a horror of dogs. He was once hunted into a cemetery somewhere on the banks of the Ganges by a pack of pariah dogs, and had to spend the night in a newly dug grave ...."