Not the same badge. Perhaps is a fantasy of the current owner, as many other details in this car.
Franco Giannini used the "Giannini" name only once, at the 1969 Turin Racing Car Show. Then the new Giannini firm owners started a legal action against him and he was forced to rename his company OTAS.
The picture below shows a 1000 GP at the show. I made a close up of the badge, that however cannot be clearly seen. My guess is it was the same as OTAS (with the Turin city's prancing bull), but surrounded by the wording "Giannini Torino".
It looks circulrar and for sure it was not the classic Frua-designed Giannini shield.