No, there is no truth in that. Your shot is in a cup wad, it stays in the cup until it is some distance from the muzzle and then falls off and the shot begins to open up. I don't know where anyone came up with stabilizing the shot but the barrel does not stabilize shot turkey gun or not. As was stated a longer barrel gives a longer sight plane, which shouldn't matter much because you don't aim a shotgun at flying or running game and it can make the gun swing smoother because of more weight forward. With modern ammo, barrel length and better performance is negligible if at all.