In Laura Ingalls Wilder's book "Farmer's Boy," one of her characters grows an award-winning gourd by intravenously feeding it milk, possibly fueling the belief in this practice.
However, the theory is just garden gossip and isn't fully supported by the horticulture community. In fact, injecting milk into pumpkin vines could actually cause them to rot.
That being said, a solution of milk and water applied to the plant's base in moderation may give a minor boost to your gourd, but excessive use can lead to negative results.