If your kids sit and study five hours a day that is at least three hours less then most public school students when you add in the time they spend on the bus and homework. If they are just mildly active during those hours they are burning off a lot of calories and building muscle that in turn burns more calories and so fourth.
The problem is not just what we eat, although I would bet your kids don't often eat a bowl of chili-cheese fries for lunch, it is that we aren't moving enough.
Kids who are home schooled have the time and the energy to be active in ways that their public schooled counterparts can not match.
You're right, you know. Although it's also true that my children watch almost zero television. A few times a month we'll rent a movie, and we frequently put in little-kid videos for the toddler. However, we're oddities in the neighborhood because we have neither dish nor cable TV, and we tune in the aerial about every third blue moon.