I agree that misquoting the statistics is the worst error. I don't think it's intentional, so I don't think it's "blatant manipulation", because in several other of her pieces I've found the same sort of easy-to-make error with other statistics--not consistently, just occasionally. My impression is that she just isn't very careful about these things if it sounds right to her. That doesn't rescue her conclusion, but it's a much milder condemnation of her character.
Regarding what the best framework is--that wasn't my point! My point is that skin color does matter. Heck, even a name that suggests a skin color matters: https://www.nber.org/papers/w29053. An older, simpler, clearer paper showing a larger effect--progress, perhaps!: https://www.nber.org/papers/w9873. Note that the two papers report different numbers in their abstracts: absolute contact rates in the first one vs relative contact rates in the second. Because relative contact rates are what you notice when talking to your friends about job hunting, I will report both in those terms: 9% higher response rate to white names in the 2021 paper, 50% higher response rate in the 2003 paper. Using names rather than pictures clarifies the issue because it avoids confounding the effect with "pretty privilege"--it is hard to make sure you've got people of equal attractiveness.
This doesn't mean that race is the largest effect, or that we want to address the issue along racial lines rather than something else, but in order to understand what to do we first should be clear on what the phenomena are. If we deny some phenomena that are real, our plans to fix things may be defective.
(It is true that the bias could be ultimately grounded in something other than race, but it is completely contingent on race, so it proves the point that there exist "privileges" that white people are afforded because they are white.)