It looks like April Ryan disagreed with him and frankly, this is really stupid. Harris clearly has African ancestry (with a black Jamaican father) and she was born in the United States. Her mother is Indian-American. There is no qualifier beyond that ... even if you want to be ridiculous and insist that you must be the descendant of a slave - nobody can prove that she isn't.
The purpose behind this stupid argument (and it may not be just the right who is making it), is to suggest that her experience as a black person growing up and living in the United States has been especially different or somehow easier than other blacks ... and that somehow discredits her from discussing the struggles of blacks for equality. That is not something you could possibly know unless you personally know her. It is very much like birther-ism, where the point was also to designate Obama something other than what he claimed to be through innuendo.
Now, some on the right might feel their own participation in this stupid discussion is validated because you can point to some blacks or some idiots on the left who are discussing it as well ... and in my opinion, it isn't.