Great idea, right? Yes, but actually no.
The presidents they invited tend to be from universities (shown as the red dots) that are a lot less successful in enrolling low-income students than they might be; this is especially true for the private universities invited.
You can see for yourself: This interactive visualization plots Percentage of Freshmen with Pell Grants along the x-axis, and Calculated Mean SAT CR+M along the y-axis. Right away, you notice a relationship: The pursuit of prestige, which means increasing SAT scores, almost assures you of enrolling fewer low-income students, as the relationship between SAT and income is widely known (and of course, correlation is not the same as cause-and-effect.)
I look forward to future White House discussions: Bernie Madoff on wise investing, The Fox on chicken coop safety, and George W. Bush on Mission Accomplishment.