I think this is exactly the thing that the authors skate right past. "Parental fears of academic competition" is assumed to be fully disjoint with "racial animus". What if "fears of ... competition" is just one way to racial animus without expressing explicitly negative attitudes on surveys?
And yes, this is a swipe at both the parent and the paper authors for not seriously considering this. The authors have literally a 2-sentence paragraph on animus and later claim to have ruled it out. And literally, you cannot take surveys at face value for something like this. People will not and sometimes cannot be honest.