I’ve also seen organizations realize in that situation that they can change or automate things as to reduce the consequences of the exceptions, or to make rules

I’ve also seen organizations realize in that situation that they can change or automate things as to reduce the consequences of the exceptions, or to make rules simpler to follow, in justifying drawing that firm line. Trust is won when people see you as being fair, and part of being fair is knowing your perspective has been heard and considered.