I fail to see how either of your anecdotes constitute racism
In the first one, a person made the argument that the sole black person in the department was there only because he was black. That's what "token black person" means. The second recapitulates a common racial stereotype about native Americans. Hope that helped!
The first side is an easy case of racism in most cases, the second side seem more nuanced. In the GP case apparently the person thought of himself as a black token, that is for sure a bad situation... but I cannot wrap my head around "how" it is a bad situation and its implications.