We travel with a couple of other families on most of our trips, and the total number of people is usually around 15, divided amongst three campsites. However, we will always pick one site and do all of our socializing, cooking and fun all together in one. No one has EVER, in all the years, come over and asked how many were actually "camping" in the site, and there were 6 or 7 adults and 6 or 7 kids hanging around one spot.
It is not dishonest, the parks are not trying to prevent a family of 7 from staying in a campsite, as many people have pointed out. You are not destroying Yellowstone or harming the environment. They're just trying to give themselves a way of breaking up parties or loud groups.
I'm sure if you spoke to someone in charge they would understand, but I would not worry about it and certainly don't alter your behavior or actions in an attempt to "hide" a seventh person. That's just crazy talk!
Yellowstone has always been my family's favorite National Park, have fun!
