Hmm. That’s exactly the opposite of what we heard from NYU itself (at a NY info session), as well as a couple of other schools, who said particularly for larger high schools they tend to discount the GC recs more as they know it’s difficult to know all the kids well.
By the way, I’m pretty sure a strong teacher rec was one of the things that helped my daughter get into NYU - her GC was new at the school and would just have written a formulaic rec.