You can't say "cotton picking mind" to a black person. Of course he would need to apologize. It doesn't mean anything if you say it to me, but it means something else when you say it to a black person. It's like saying "your Momma" to a friend who is an orphan. You can't be that tone deaf. That being said, we should all be able to say "that's an honest mistake" and walk away after he apologizes.
**** happens. I said "run boy" to a black football player on the TV with a black friend there. I did not mean anything by it. It's seriously the most harmless thing you can say that can be construed as racist, but I still apologized to him immediately and said I didn't mean it that way. He accepted and said he knew my intent and wouldn't be offended either way, but it was no sweat off my sack to apologize, in case I had offended. This is how adults adult.