When a parent directs a teen to only consider top tier colleges, that parent needs to plan to play big bucks. Although it does happen that some students I work with are at top tier colleges with significant tuition discounts, it is also possible that they will be offered admission but not enough scholarship money to make that college affordable.
A variety of college targets is the best strategy. It allows parents and students to "shop" for colleges. Less well known colleges sometimes have the best program in an area and are sometimes able to be more generous with scholarship money than public universities.
My experience of over a decade in college admission and scholarships is that the largest scholarships students receive come from the colleges themselves. Students who only apply to hard-to-get-into colleges, are less likely to receive financial aid.