Well, because TVTool doesn't initialize the TV output like Nvidia control panel does. TVTool goes directly through the TV chip. The Nvidia control panel calls the bios, to call the TV chip, to call the TV out.
But Nvidia also uses the bios/drivers to recognize the settings of the card. And when the Bios is incompatible with the drivers, the Nvidia control panel/drivers can't recognize the Tv chip.
While you need a 21.xx driver of before to work the TV out with the current bios, it's not a "Driver problem".
Back when MSI had a huge outcry because their GeForce3ti200 TV out wouldn't work with any drivers except 21.xx, I was the one to figure out the Bios problem and solve it. How? Using the reference Nvidia GeForce3ti200 bios.