You are right, @lookingforward . A lot of this discussion, including my input is Quatsch. If you want to to apply to school, you want financial aid, you make your own determination as to whether it’s worth the application to apply as a need applicant if you can swing it without the aid you might get. If you don’t believe what the college says in this regard, then you proceed with the process without believing.
If not accepted to a school when you’ve applied for aid, you can always think of that as a reason you did not get in. When you are full pay, that one doesn’t fly.