You weren’t directly involved in that discussion, so we can’t know whether UConn’s offer had anything to do with that student getting more merit from the private school, maybe they would have given more merit anyway because the private school really wanted that student. And that’s often what underlies successful appeals for more merit/discount…the school really wants the student to commit.
Of course being respectful in these discussions is necessary, nor would I communicate/make the AO feel that they are in a ‘negotiation’.