Access to the nation's most selective colleges remains starkly unequal, with students in the lowest income quartile constituting less than 4% of enrollment. A popular explanation for this phenomenon is that low-income students "undermatch" by attending less selective colleges when their credentials predict admission to more highly selective colleges. We identify three problematic assumptions in research on undermatching: (a) that researchers can differentiate colleges at the "margin that matters" for student outcomes; (b) that researchers can accurately predict who will be admitted at colleges that use holistic admission processes; and (c) that using achievement measures like SAT (Scholastic Assessment Test) scores to match students to colleges will reduce postsecondary inequality. We discuss the implications of these assumptions for future research on college choice and stratification.