I think they're referring to muscle weighing more than fat so factually then yes there is a chance you may stay the same if you are gaining muscle, but that doesn't mean you won't be losing fat as well. You will be losing fat but adding muscle which will affect the numbers you see on the scale.
My boyfriend does mainly weight lifting and he has very muscular arms, shoulders and back; his weight is around 16st at the moment and while he does need to lose some weight from his stomach area (which he is) most of his weight is muscle so even when he loses the weight he wants to it won't affect the results on the scales too much.