This may be an overstatement with a grain of truth behind it. For example, Columbia promises to meet need (as it defines “need”) for frosh and regular transfers, but does not guarantee to meet need for 3+2 program transfers.
However, many of the best financial aid colleges are highly selective, and some take very few transfers. So a college GPA significantly less than 4.0 will be a problem in applying to those colleges. In addition, they tend to have about half of their undergraduates from non-financial-aid families, similar to Amherst.