If a school, say, Princeton, were to know your top choice were Harvard, would Princeton turn you down (assuming you were totally qualified). Also, do schools communicate as to which applicants have been accepted to different places?
How would they find out?
The only communication about where people have applied is when schools exchange ED lists so that they don’t admit applicants to RD that already have binding agreements. They don’t discuss specific students with each other in the RD round; the acceptances are independent of each other.
Even if Princeton knew your top choice was Harvard, they don’t know if you’d get in there, and if you’re talented enough to impress Princeton’s admissions committee, they’d want you to come to Princeton. HYPSM don’t have to worry about yield like some less prestigious schools.