Actually, yes it does.
I'll say it once more, and then get on with my life. You're too silly to waste any more time on: Barnes dominated Sampson in two seasons out of nine. Sampson dominated Barnes in five seasons out of nine, and they split two seasons.
One of Sampson's season sweeps of the horns' came after Barnes' two strong seasons, so it was Sampson who turned it around. There is no guarantee whatsoever that, had Sampson stayed, Barnes would have begun winning again against Sampson. In fact, the only evidence we have suggests otherwise. Sampson led by a huge margin -- 16-7 -- in the overall head-to-head, and in the final two seasons they faced each other, he won three of four.
Yeah, Barnes really had it turned around, all right.