In the story, Grandma Dowdel gets away with lying by using her age and life experience to her advantage.
Throughout the book, Grandma often uses white lies to maneuver her way around difficulties. In the story about Shotgun Cheatham, she manages to lie to the reporter because she's able to turn his biased perception about country folk to her advantage. Additionally, because of her shrewd ability to correctly assess the characters of others, she's able to tailor her lies so as to appear credible to her listeners.
Playing upon the reporter's presuppositions about gossipy country housewives, she tells the reporter that Shotgun Cheatham served with the Illinois Volunteers in the Civil War and that he was with General Grant when the fortress city of Vicksburg, Mississippi fell to Union control. On top of these two lies, she maintains that it was General Grant who gave Shotgun his nickname. So, in one instance, Grandma Dowdel manages to change Shotgun from a "kill-crazy gunslinger" to a Civil War "war-hero marksman." While this is no mean feat, Grandma Dowdel only gets away with lying because she knows how desperate the reporter is to craft a newsworthy story for the sake of his career.
Later in the book, Joey is horrified when Grandma Dowdel tells Ernie Cowgill he's part of a Chicago gang and "meaner than he looks." After all, Ernie, although the smallest of his brothers, is still an intimidating figure, and Joey is afraid of the repercussions that may result from Grandma's lies. Grandma Dowdel is unperturbed. She insists she only lied to protect Joey and since Ernie Cowgill is only in the fourth grade (despite being almost sixteen), he'll believe anything he hears. The implication is that Ernie is too unintelligent to comprehend she lied to him.
Grandma Dowdel gets away with lying by shrewdly assessing the nature of her victims and using others' perception of her to her advantage.