Were there advertising agencies in the 1960s which only had white people working there? If the answer is 'no' then she has a valid point to make. If the answer is 'yes' then not so much.
The "answer" is irrelevant even though I'm sure there were some blacks employed at ad agencies in positions other than secretaries and mail room employees even in 1960's New York.
Mad Men is about Don Draper and his life, his ad agency, advertising and ad agencys in the 1960's, and the 1960's. None of that precludes stories with black people in them. They don't have to show blacks in positions of power or in positions like Draper's in order to feature them in stories.
Don, who is cheating again, has an affair with a black woman--it turns into more than he expected. Roger has an affair with black woman... Pete has affair with black woman... More provacatively, Peggy has affair with black man... The agency gets into financial trouble, sees advertising to blacks as a way to quick bucks with no competition -- hires black person to culturalize creative staff. They could do a story featuring Don's secretary.
Hell, even I can come up with easy ways to include black people. I'm not advocating this, but thinking that Mad Men doesn't produce stories with blacks because they can't
-- because the show is set in the 1960's -- is simply incorrect. It is because either AMC doesn't want it or Matthew Weiner doesn't or both.
But to be fair, in the first few seasons the show did have some stories with blacks. It has only been in the last couple of seasons that it has appeared that there are no blacks on Mad Men.