Having worked internationally (Asia and Europe), I don’t disagree that having a Harvard (or Princeton or Yale) degree doesn’t give you a leg up over lesser known but excellent US universities. But I think that is limited to business/finance/consulting/law. The reason is for these businesses, they are also sensitive to name recognition on the part of their clients. If you are pursuing science and engineering, IMO the employers will be much more aware of the strength of the science and engineering departments of the US university vs general prestige and name recognition.
I don’t think there is an REA advantage of any of the 3 vs the others. I do think that you should pick the school that you are more excited about as it is likely you will write better essays and short answers for that school.