Strictly speaking “insufficient financial aid” is always a valid reason - and with NYU’s NPC being so bad (the only upper income category is 99k+, whereas paying 80K would be a huge difference for a 100K and a 300K household) that’s why they’re quite willing to let ED obligations go.
But once an applicant says “no - insufficient FA”, that’s it.
And bc some GC or HS could get “black balled” by universities if an applicant takes back their commitment to attend another university, some GC can take action. It can get messy.