As far as management's interest in the situation, it would probably be helpful to know the context a bit more. Did she offer this customer substandard service because of his/her race? Was there ANY CHANCE that another customer might have heard the comment? If the answer to either question is "yes" then that's something I think management would want to know or should know. I will admit that I sort of read the first possibility into the OP's question. Rereading it, however, that wasn't correct.

I will agree that with you that the comment is likely not actionable from a legal standpoint, at least not in isolation. However, comments like that can conceivably create a hostile work environment and from that standpoint, should not be tolerated or encouraged from a managerial standpoint.