Davidson had a reputation for never mincing words. She would always say what was on her mind. When she ran for reeve in 1960 she called one of her opponents, Leslie Saunders, "bigoted, pigheaded and, in his attitude to women, a throwback to the stone age". During the East York mayoralty race in 1966 she called Beth Nealson a "wish-washy, prissy, sweetheart". Metro chairman Fred Gardiner once complained that she had "taken a yard" off his back. Davidson replied that he still had plenty of hide left to spare. She referred to Metro chairman Albert Campbell as a "maundering chairman, inclined to regard other councillors as grade one dunces ruled by himself as schoolmaster." In one exchange with Campbell, she retorted "Don't be addled man. Don't talk stupid!" Nevertheless, she had her supporters. Fellow Metro councillor, Bill Kilbourn spoke fondly of her. "Decent, fearless, independent. True was a thorn in the flesh of the smooth men at Metro (council)."