TL;DR: Yeah, the white racist could be less privileged OVERALL than the OP, but not in any way that counts in this interaction.
It does matter if you are trying to understand the incident in context. The actual, literal, questions:
Why do some white guys do this?
Because some white guys are racist.
Is this the defense some white men use when they are rejected by a person of color?
Yes.
It's almost pointless to answer those questions because they are so obvious.
But I can't believe the OP just wants a literal answer to such a basic trivial question. I have to consider that the post is framed so it goes beyond the literal and implies larger questions.
What could be the unspoken questions then:
Are all white men like this? At least to a degree?
I bet you a dollar the guy was wearing shoes when he opened his racist mouth to the OP, but the OP does not ask "Is this the defence some men who wear shoes use when rejected by a person of colour?" because that would be ridiculous and everyone knows shoes have nothing to do with it. But you wouldn't bring it up unless you wanted to go there. So by focussing on whiteness we are automatically into the land of exploring whether whiteness is innately linked with racism. The question asks if there is something inherent in being white that is racist. Wondering if there is no way to be white except by being racist.
Well the answer to that is "No, of course not." Followed by "Was this just an excuse to imply that white people are all racist? If so that is some lame shit on tap. But if you have sincerely never met a white guy who was not hiding a racist asshole just under the surface, you need to move to a different country." Which is about as far as I can go with the effort it takes to push aside my cynicism about the sincerity of this question.
I will say the question does a definitely useful thing. It bears witness to remind us that racism is not yet extinguished. Good reminder, especially for people who have never been on a blind date with a racist. In my community, there are people of every ethnicity who have never been on a blind date with a racist, but clearly that is not true everywhere.
But it reveals that many people know as little about white people as they claim white people know about their experience. Which brings us to the broadest possible context, and a discussion of privilege:
No, it really doesn't. When a white person uses the N word to a black person, they're using privilege as a weapon. This is true even if it's a poor white guy in Arkansas talking to Oprah.
When it comes to OVERALL advantage, there's this thing called Intersectionality; obviously Oprah is more favored by society overall than the poor white guy in Arkansas, because enough money buys any level of privilege (and also she's famous and accomplished). But it was a harder road for her than it would have been had she been white, with everything except her race being the same.
In most cases it's more complex. If I walk down the street in NYC with a black man, he's dramatically less likely to be stop-and-frisked than if he's alone, or with another black man. My white privilege covers him, in other words. If we hold hands, we're still probably immune from S&F, but more likely to get beaten up by anti-gay thugs.
First, being able to walk down the street minding your own business is not a privilege. I get that in some place people really can't do it without harassment. But the idea that this is a privilege is to give up on the idea of rights and freedoms. Privilege is the wrong word and a product of a dangerous misunderstanding of human relations and the law.
Second, the idea that you can rank people on a scale of privilege based on their colour is out to lunch. It is obvious, and I'm sorry, laughably so, to suggest that John McWhorter had a harder row to hoe than some white kid living in the fifth generation of uneducated poverty in some rural backwater. It doesn't matter to that white kid in the sticks that George Bush's father opened doors for him. As you say, in most cases it really is more complex.
