This is in fact completely wrong.
According to both of them, Ballmer has been fully in charge of Microsoft in all respects for more than a decade. Further, Gates has been completely retired from any decision making role in operations at Microsoft for five years. For years before that he was a glorified software opinion giver ("chief software architect"), and by his own statements he was heavily ignored in the role.
If you have something that proves otherwise, given we have their public statements (over and over again) on the matter, I'd love to see it.