Be careful with that assessment, because many of the places with great financial aid are not actually the best at recruiting or enrolling students that are great but have lower income (there was an article that explored this). What Vandy does more effectively and perhaps strenuously so is making it easier for upper middle class and middle class people to avoid huge loans (a worthy endeavor indeed as often these folks get screwed over). However, supposedly many more schools help out better with actual low income students, not necessarily through financial aid programs (though basically all of them now have it such that those below 50-60k attend for free), but through more aggressive recruitment and selection of Questbridge Scholars for example. The bracket targeted by Vanderbilt means that they likely want to yield those with higher scores and NM status more than anything else. Many other schools with a strong score range (I would say averaging at least 2000-2100) that is not as high tend to select and yield those in lower SES backgrounds in higher numbers. It doesn’t seem to hurt them that much either (Stanford is among such places along with several LACs). Places like Vanderbilt perform strongly (in enrolling), but not as strong as the financial aid offers would predict I think: http://www.washingtonpost.com/local/education/amherst-a-leader-among-elite-colleges-in-enrolling-students-who-need-pell-grants/2014/03/25/9df8ab6a-b414-11e3-b899-20667de76985_story.html
Many of the schools above it I think actually have weaker or very similar financial aid program so it is some mixture of differences in the selection processes and whether or not the students who are admitted want to yield. My theory on stats clearly isn’t what is driving these differences though as Chicago does a little better than Vanderbilt, and WashU is just …not doing well at all (so maybe that model more so applies to them). Some complicated stuff is at play.