First thing to remember is that those are the numbers of kids who have an SAT of over 1400. So, when we are talking about actual number or even percentages of the college students, there are fewer of the bottom 20% than there are of the next three quintiles.
That number, of course, is because the bottom 20% are considered URM, though, looking at the numbers, the entire bottom 40% should be considered URMs. However, as others have pointed out, kids from the second lowest quintile cannot be put on a college’s brochure as "X% Pell Grant students…
Overall, looking at the percentages, I would say that the missing middle is divided into two parts. One part, especially those between the bottom quintile, cannot be accepted since they lack ECs and other accomplishments, even if their SATs and GPAs are high. They and their schools can’t afford to train and send teams to athletic or academic competitions, the families can’t afford to have their kids be part of clubs, etc. They can engage in ECs, w\but when places like Harvard are looking for kids with national level prizes, and kid from a lower SES family attending a lower SES school won’t have those. A kid at the lowest 20% will get a URM boost, but not a kid from a family which makes more than that, but not by a lot.
When you get to the lower income levels which can afford these, other issues kick in, such as the fact that a family can technically afford the CoA, they cannot do so realistically. Even if they can, with loans, or by cutting their own costs, these are middle class families, and a basic middle class philosophy is that if you pay for something, it should have the values of the money or more. For most families in this income range, with high stats kids, there are college option which cost far less. Why should a family send their kid to Yale for $300,000 when they can send the kid to Arizona for nothing (and the kid gets money for books) or to UMN for $60,000?
Only at the top 10% does the cost of the tuition that a family has to pay no longer become an important issue, in general, compared to the prestige or social status that attending such a school provides.
Not to say that there aren’t lower income families who think that a $200,000 debt is worth it for their kid to attend Princeton, or tha there aren’t families who are in the top 10% who think that the money spent of attending an ivy would be better spent elsewhere.
Finally, just because the graph divides income to quintiles doesn’t mean that the the boundaries between actual income groups looks like that, or that there even are clear boundaries. A family which makes $135,000 a year is similar to a family which makes $125,000 a year, but very different from a family which makes $500,000 a year, even though the first is in the fourth quintile, while the latter is in the top quintile, like the family making $135K.