I feel like that varies depending on where they grow up? For one, I imagine an upper-middle class suburbanite would feel a lot more "undeservedly privileged" than a farm kid in Alabama, and so on and so forth.
Why the hyper-focus on the amount of melanin in their ancestors' skin, though? Sure, there are certain cultures that achieved much, but obsessing over race ignores the substantive issue, that being the culture that produced these achievements.
When much of the Media makes a point to talk about this, mostly in a consistant way, people are going to react. There's only a few ways
to react.
For most of human history, it was tribal, and that was some genetics, and some culture. There were often other tribes around with similar genetics and culture, but they weren't
yours. That was healthy, caring about your family more than your neighbours, and caring for those outside that, less still.
As nations got bigger, all that stretched. But, still, you could have that sense of extended family, with ethnic divisions being there, but smaller than it might be. The euro empires, for instance, had ethnic elements, but there was a real sense of responsability for those who were part of it, even if they were different in that sense. "We're all Christians", "We're all part of the Commonwealth", "They might be wogs, but they're our wogs.", etc.
So, right now, who's even allowed to say "My ancestors were part of ending slavery, I should be proud of that." without being attacked over it? And, before you ask, I have been attacked over that.
We're not allowed, in the greater cultural sphere, to have anything that unites us. Not skin color, not faith, not even cultural touchstones. Not unless said factor can be used to break things further. There's a reason why insanity and depression is so common right now.
That's why Black Power groups are fine, so long as they aren't violent, and sometimes even then. And White Power groups are the kind of thing that'll get you attacked by pretty much everybody.
So, to boil down your question to a simpler answer, it's not about melanin. It's about desperately looking for something,
anything, that makes you feel like you could have
anybody on your side. And ethnic traits are something you can tell at a glance.
Besides, racism is built into our very instincts. Trying to break that is just dumb.
Oh, and the farm kid Vs the suburbanite? The farm kid'll do something real, and thus get an entirely different look at the world, than the suburbanite. So, yes, somebody in the real world is more likely to see the truth.