@Cverdugo is spot on with his example. "Rivals" only matters of they are closely ranked. Fsu vs UF for example. As he said, you will get laughed at trying to use Michigan State as a bargaining chip against Michigan...
Sorry I didn't see your comment earlier, @MikeyMangood. @twssmith is exactly right. A LOCI is a letter of continuing interest; you should consider sending one if you've been waitlisted.
I don't BR immediately after I take a PT. I usually PT in the morning and BR at night. I usually complete my BR the following day. I think giving your mind time to decompress is a good thing, and you see the questions again in a different state of mind.
I think super splitters are viewed the same, but someone with a 3.5 from Williams or Princeton is likely to be viewed more favorably than a 3.5 from a state school