City Councilman John Liu is running for Comptroller and, in a TV ad, he says he's worked in a sweat shop with his parents. However, a Daily News reporter wrote yesterday that he never did, based on what Liu's mother told her: Jamy Liu says she never worked in factory, though she did bring home fabric; her sons helped her with and were "paid 25 cents for every ball he spun on a yarn-spinning tool," money that Liu's father Joseph said was "allowance." Liu fired back, with a statement on his website, calling the News piece "gotcha" journalism, "My mom was very reluctant and embarrassed to talk about her experience working in the garment industry," and noted that many sweatshops "including the one my mother worked in - combined factory hours with home-based piece work to maximize the exploitation and squeeze the most out of workers: even after leaving the factory, the work never ends." Today, the News stands firm and wonders why Liu "initially said his mother worked in a sweatshop while her children were 'latchkey' kids. Now he claims she worked at home during the school year, but brought her boys to the factory during the summer." Related: Liu fires shots at Councilman David Yassky when asked by the News to discuss his rivals for the position.