So, are you saying a tuner cannot effect the horizontal in a group?The tuners mass at the end of the barrel induces a larger droop in the barrel due to gravity and adds to the droop present from the barrels own weight. But the muzzle is an anti node putting that mass on the anti node dampens harmonics. Think about touching the open end of a tuning fork vs letting it ring free. The vibrations have to move more mass so unless they are given more energy to start with (more droop in the vertical plane) they will have less amplitude since they have to move more mass.
Since the tuner does nothing to add to the horizontal imbalance of a rifle barrel it does not induce stronger horizontal vibrations. Since the horizontal vibrations are the same strength with and without the tuner (close enough anyway) the extra mass of the tuner preferentially dampens those vibrations.
Tuners add to the vertical imbalance in the barrel and induce more energetic vertical vibrations. But those increased energy vibrations have to move more mass again so the net effect is near a wash in terms of amplitude (can be rifle dependent I think so ask a manufacturer for sure) but now you have eliminated some horizontal and gained more precise mechanical control over where on a vertical vibration wave your bullet leaves and lengthened your tuning window. These things are a significant benefit.