That's literally what I said. Good for you.
That's what you said in the first sentence of the quoted paragraph. I was specifically addressing "actual episodes might be different" in the second sentence, saying that part seems unlikely.
However, I have to rethink that after doing some research. Apparently, Samuel J. Battle of the NYPD became the first African-American parole commissioner in 1941. It's not the same as being a full-on police commissioner, but it goes to show that it's not out of the question that there could be people of color in positions of authority in a '40s setting despite the presence of systemic discrimination. I doubt they'll go that route, but I concede that it's not impossible.