Competitiveness is definitely the last thing that I look for in a professional athlete.
Seriously though, I think your point's a good one, and fair to make. The Pats have proven willing to take chances on guys with some character concerns who sometimes fail to work out within their culture. Sometimes it pans out to the tune of Randy Moss or Corey Dillon, and sometimes you get Chad Ochocinco or Albert Haynesworth. It's a risk that the Pats are willing to take, and I generally agree with their philosophy, so I don't even necessarily see it as an organizational criticism to observe this fact. It's just something that warrants mentioning.