I think great deal also has to do with advocacy. The middle class and above mother as the knowledge, time, and resources to advocate for her child.
As a teacher who teaches in a low-income school, there are many factors at play. Many of the parents speak no English. Their main concern is to get food on the table. They think that the school is naturally doing what's best for their child. However, this is not always true. A child in this situation could have high potential but due to circumstances (limited sleep, limited exposure, ESL, food shortage, etc.) will score lower on assessment tests the district uses making it seem like he/she is below the gifted cutoff.
The curriculum and opportunities play a part as well. Higher income school districts have more staff, lower class sizes, more advanced courses, and gifted programs. While I am aware the quality of each is often lacking, I think we can agree that simply having a gifted program acknowledges a step in the right direction. Lower-income schools have no gifted program or limited advanced coursework. Textbook and Testing companies are also ravaging these schools. If they school low on assessments, curriculum is swapped for heavily scripted lessons. One district moved to a "Reading First" curriculum that had curriculum representatives force teachers to remove all their trade books and only use the supplied reading basal, because we all know that to increase reading we limit student reading interactions?! This creates a cycle where they score well enough on the matching assessment, but still do poorly enough to warrant the continued use of the company.
Long story short, I think advocacy plays a huge factor. For the most part, middle-class and above families know how to fight for their child's education.