Although the survey was done by household, the numbers in the data set represent individuals, not families. I can't replicate your football result in a search, but depending on the keywords used, I got soccer, football, basketball, and baseball all as answers to the question of the most played (not most popular) sport in America. Like everything, it depends on wording and methodology. So I'm going to stick with figures measuring people actively involved in organized sports, since that seems to me to be the best way to do it.
But ultimately, it doesn't really matter. All that matters is that it's still a very popular sport for American athletes -- no one disputes that -- and the media miss out on a huge opportunity by continuing to ignore a fan base that could be easily cultivated. That's the real message people should take away.