I can't read the article - do they explain why they think this is a "paradox"?
Personally, I don't think they actually believe it's paradoxical, I think the authors are just trying to be polite to those who criticize standardized testing with identity politics. Politeness can aid in persuasion, so I don't blame them.
This doesn't exactly answer your question, but MIT added test scores back recently and wrote a blog post explaining why: https://mitadmissions.org/blogs/entry/we-are-reinstating-our...
I think the "paradox" is that you'd expect disadvantaged students to perform worse on standardized testing.