Not necessary, because the author’s reasoning relies only on the relationship between obesity and amount of TV watched. This doesn’t commit the author to a belief about “sedentary lifestyle” or what is the “most important” cause of obesity. As long as amount of TV watched is positively associated with obesity, the author’s reasoning can work.

The author doesn’t have to have any belief about “cable television.” The author’s argument concerns “interactive television,” and makes no mention of other kinds other specific kinds of television.

Not necessary, because even if genetics can significantly contribute to obesity, it’s still the case that amount of TV watched is positively correlated with obesity, and that correlation can still support a prediction of more obesity as more TV is watched. Although the author does have to assume that other factors relevant to obesity don’t decline after interactive TV is introduced, that doesn’t mean the author needs to think there are no other significant factors that cause obesity.

Necessary, because if this were not true — if the children will NOT increase their TV viewing with the arrival of interactive TV — then we have no reason to think that interactive TV will lead to an “increase” in obesity.

Although the author does have to think that TV watching among children will increase with interactive TV, that doesn’t require the author to have any opinion about “universal” availability of TV or how quickly that will be achieved. Even if it takes longer for interactive TV to be universally available, the introduction of it can still lead children to watch more TV.