I wouldn't say that Bryant's quoting MLK, Jr. is proof positive that he's playing the race card, but I do understand why some people might have good reason to think so.
1) It's difficult at this point to tell whether his defense team will focus on a "sluts or nuts" attack against the girl or a "play the race card" attack on the sheriff's and district attorney's offices motivations and investigations. They've leaked information pointing in both those directions, but Kobe's use of that quote at the Teen Choice awards could reasonably be construed as evidence that he prefers the latter route.
2) I think it's even more reasonable for someone to be offended by the inappropriateness of his use of that quote if they know the full history and context of the quote. It was just a small part of his Letter from Birmingham Jail in 1963. In it he was responding to some other clergymen who thought his civil rights activities in Birmingham did not show good judgement:
"Few members of a race that has oppressed another race can understand or appreciate the deep groans and passionate yearnings of those that have been oppressed, and still fewer have the vision to see that injustice must be rooted out by strong, persistent and
determined action...."
...?But more basically, I am in Birmingham because injustice is here. Just as the prophets of the eighth century B.C. left their villages and carried their "thus saith the Lord" far beyond the boundaries of their home towns, and just as the Apostle Paul left his village of Tarsus and carried the gospel of Jesus Christ to the far corners of the Greco-Roman world, so am I compelled to carry the gospel of freedom beyond my own home town. Like Paul, I must constantly respond to the Macedonian call for aid. Moreover, I am cognizant of the interrelatedness of all communities and states. I cannot sit idly by in Atlanta and not be concerned about what happens in Birmingham. Injustice anywhere is a threat to justice everywhere.?
Somehow, I just cannot equate Bryant's situation with that.