But all of the characters have crappy things happen to them, no matter their backgrounds. All characters generally have crappy things happen, otherwise the drama would be dull.

And I think 'introducing Martha' = 'only one minority character' is reading far too much into the 'text.' Martha and Tosh wouldn't necessarily have much contact; she was working mostly with Owen on the medical matters, and she and Jack had a pre-existing relationship. Tacking a scene in just so two characters who happen to be minorites can interact wouldn't make sense (and would probably feel completely tacked on).