It really depends what “second tier” means here. Typically, attending a university where one’s SAT score is +250 or +300 above the average is not a good idea. So, if the choice really is a mediocre directional and a top 25, AND the parents can pay, that’s an investment that’s worth making in my opinion.
As for grad school: any PHD program will be funded.
Med school, law school… it depends what the college is.
I agree that the student should find 2 safeties they like before proceeding with ivy plans.