I think I see your point. Ms. Cosby is not playing the race card, because she genuinely believes that he is innocent. (Although I believe she is mistaken, even if understandably so.) But suppose Mr. Cosby had said this himself, knowing full well that he was lying? Or consider Clarence Thomas, who described his Supreme Court hearings as a “high tech lynching”, to deflect from the sexual-harassment charges against him. I would call this kind of deceitful manipulation of racism-caused pain “playing the race card”.
As I think this through, I realize that my definition is a lot narrower than most other people’s. It certainly doesn’t apply to the example mentioned in your article. You were expressing your honest feelings about how the sight of a confederate flag made you feel, and the decent thing to do would have been to apologize and not display the flag anymore. Talking about race, or the pain of racism, should not be seen as playing the race card.