Skuzzy, this is just a guess on my part, but I would say you weren't raised down South. If I'm wrong I apologize.
Well, I was, and I can say from personal experience that Shaky's assessment is spot on.
The association of black people with watermelon and fried chicken is one of the oldest caricatures in Southern culture. I've heard those jokes all my life...and they ARE racist.
One doesn't hear those jokes as often as you once did...but occasionally you can still hear some "grown-up" (In this case, the word is an oxy-"moron") repeating one and s******ing like a teenager telling pornographic jokes in a gymnasium locker room.
Certainly the professor knew what he was doing...taking a jab at a prominent republican with a problem laced with racist inuendo.