I think a live debate is a highly risky operation, especially if the debater is not used to speaking in front of the camera. It is incredibly easy to screw up and say something stupid, and once you do, it's out there, with your name on it. A great opportunity to look like an idiot on YouTube forever. It's also incredibly easy to say things in a way that makes it easy to change their meaning by taking them out of context, which can be done deliberately, or just out of carelessness by the producer.
A prepared statement or video shoot, with the opportunity to redo it if you stuff it up, is in my opinion the much safer option. There's a reason why politicians who are trailing in the polls want to have debates, and politicians who are leading prefer to avoid them - the debate is an amazing opportunity to stuff things up.
I recall watching an American news presenter "debating" someone who (while the South African government still had apartheid) wanted to partition South Africa along racial lines. The American, as nearly as I can tell, seemed to have assumed that his opponent was going to have horns growing out of his head and talk like a raving lunatic. Unprepared, underestimating his opponent, who turned out to be quite smooth and well-spoken, the American made several extremely foolish mistakes during the debate and ended up looking like a complete idiot.
Debates are risky. When you have the facts on your side, it's best to have a controlled environment to the extent possible. When all you've got is bull****, the chaos and volatility of a live debate are your friends.
