It does mean they are confident that the rates are different for men and women in Gen X

Umm, surely not? If the confidence intervals overlap it means that they are not confident that the rates are different, doesn’t it? Of course, it also does not mean that they can say they are confident that the reading rates are the same.

So the statistically sound way of saying it is that the null hypothesis is that reading rates are the same, and their study has failed to reject the null hypothesis.