Good catch.
Between you and me, I'd say that sandwiched between "not a brawler" and "rules well his own house" I can almost see the wheels turning in Paul's head as he switches gears from 'things that affect the man's relationships with others' to 'things actually under the man's jurisdiction' to the most intimate, internal problem: pride. If you're not coveting other people's stuff, you get into less brawls, and really you should be minding your own business anyway, which we can now talk about (rule your own house, manage your own children, and keep a lid on your pride if you're doing it well).
So in other words, I'm content that my argument based on the main thrust of Paul's argument is still solid, and I'm not sure (very personal, just my opinion) Paul was even thinking of covetousness in the 'commandment' sense there anyway, just thinking of regular sort of day-to-day 'misdemeanor' covetousness....
However, if I were in a hostile situation, and somebody thought they had just scored a major point by pointing that out, I would just quickly concede the point. Makes you look reasonable.
And I tend to favor big picture, "what's the big idea" arguments anyway, as I find that most people don't have the attention span to follow long, convoluted, detailed presentations, and more importantly, the kind of guy that's going to make this connection and think that therefore this passage prohibits polygamy, therefore the whole bible prohibits polygamy, therefore God hates polygamy, etc, is not the kind of guy I should have been talking with in the first place anyway.That's a real peek-behind-the-curtain kind of explanation (might have too much coffee circulating...), but it's a long way of saying your are absolutely right but I'm probably not going to change the webpage.
While much of our thinking and memory is actually imagery, I think a big chunk of my brain traffics in song titles and lyrics.... 
