The point of the women story was that the bank changed it's judgement not before it had received the relevant information (she was from out of town and had been phoning and writing the details to the bank) but only after it had become aware of the irrelevant piece of information of the women racial origin. Up until they met her the bank was happy with her status.
And, of course, jo is right to point out that there is no need for the redundant white, I still contend that this redundance is motivated, possibly sub consciously, by racist thinking.

It has to be said that many words and much language reflect racist thought through many ages. A large number of abusive term used are racist; philistine, vandal, pillock, bugger, tory, hooligan are some of the less obvious. Then there is the way that fairly straight forward early english words have become taboo since the Norman conquest to be replaced by french and latin terms and euphemisms. There are still many sections of the british working people who use a -house rather than a toilet but their, original, germanic, language is frowned upon by many.