I guess there are multiple aspects of "character" - the article mentioned the factors as being: "...maturity, work ethic, intelligence, citizenship, coachability, responsibility, trustworthiness, accountability, leadership and overall intangibles." While Carr might have done well in some of those, he was not "high character" in others.
For someone who was almost the inverse of Carr, you have Michael Irvin, who lacked in most non-football areas, but excelled in areas such as work ethic. Clearly no one would label Irvin as a "high character" guy, but yet overall, considering all of these aspects, he might come out closer to Carr.