This statement that Vera is capable of "romance at short notice" is Saki at his satirical best. According to the American College Dictionary, romance is
A tale depicting heroic or marvelous achievements, colorful events or scenes, chivalrous devotion, unusual or supernatural experiences, or other matters that appeal to the imagination.
So, Vera—whose name is ironic since she rarely speaks with veracity, or truthfulness—has now fabricated another tale. This tale is from the real instance of the "tired brown spaniel," using a "colorful" fictional event: Nuttel was hunted by a pack of dogs on the banks of the Ganges. Thus, although this story is set in a faraway land, it is anything but heroic given Nuttel's deeds and experiences.
Vera is capable of blurring the lines between imagination and reality as she entertains guests of Mrs. Sappleton. Her story about the males of the Sappleton family who went hunting and were lost resides between truth and fiction. Later, rather than depicting the guest, Framton Nuttel, as capable of great achievements and "chivalrous devotion," Vera satirically portrays him as a weak and cowardly man who has been pursued by vicious dogs and spent the night in a freshly dug grave to escape injury.