Correlation is not cause and effect.
Moving the cg aft also increases the minimum control speed. Would you argue that decreased tail trim load causes increased VMC? I hope not.
Consider this example:
I take a delta-winged type - let's say a Mirage - and put a tailplane on it (maybe top of the fin?)
Now, I trim the aircraft in level flight, using the conventional Mirage trim system of wing t/e devices. I control tailplane angle such that there is ZERO tail load.
Alongside I fly another Mirage, but with no added tailplane.
The tailplane is carrying no load, yet I absolutely guarantee that it is making the aircraft more stable in pitch, as you'd be able to see if both planes were hit by the same gust.
In fact, I could mistrim the t/e surfaces to induce either an upload or a download on the added tailplane, and the "tailed Mirage" would STILL be more stable than the conventional one.