The rep was correct in saying the GC LOR is the most important Rec. Certain key words, certain evaluation are sought on the apps from the GC. The GC is supposed to be the objective judge of all of the students in the school. You can pick your teacher. Most of the time, not the GC
My kids school gets nearly 100% accept at NYU. I think audition and portfolio schools programs excepted and it’s through some program sometimes, but yes, if GC says NYU is good, it’s a go.
I don’t see why anyone is surprised about the GC REC being so important