As to the original source of that statement, it's hard to say, and I couldn't find it. But I do remember reading about that, and it is mentioned in several articles in the context of his teaching a writer's workshop with the author John Cheever in Iowa City in 1973. It was a period of heavy drinking for Carver, who was an alcoholic. Themes of alcohol are reflected through much of his writing, and his short stories in particular.
It cost him jobs and likely his first marriage. Three and a half years after that workshop, in 1977 Carver finally entered treatment and went to AA meetings. He was mostly sober until his death in 1988 from lung cancer, and most of his best writing (in my opinion) happened after he got on the wagon.