Those places have even less to offer, to such an extent that a fresh diploma from such a school is damn close to a negative signal for intelligence and competence. (If not already past that threshold!)
If anyone's treating attending a non-Ivy school as a negative signal for competence, I can only treat that as a negative signal for their competence.
> Please understand that this is in no way a judgment of you as a student or as a person, since our decision has more to do with the applicant pool than anything else—many of our applicants are not offered admission simply because we don’t have enough space in our entering class.