The hay is part of it, but some animals just smell good. Vegetarian species are often likely to smell good. Lots of parrots smell really good, especially c*ckatoos and amazons. Most co ckatos have a somewhat sweet smell, but Moluccan's are my favorite. They smell like maple syrup. Most Amazons have a somewhat spicy sweet smell.
Parrots so consistently smell good that if they smell wrong, I look for problems, usually with the GI tract, but sometimes it's a metabolic problem. If they keep smelling "off" even when blood work and stool checks are normal, I keep looking until I find out what's wrong, cuz they don't stink for no reason.
There is a group of birds called Pionus parrots (related to Amazons) that are reported to smell either very nice or like dirty sweat socks. In my experience, the "sweat socks" birds have something going on, because often after resolving health problems they smell good. I've had owners tell me their bird never smelled good, always like socks. Then we treated and the bird smelled nice for the first time in it's life.
If you know anybody with a Pionus that smells like socks, tell them this and make them take their bird to a GOOD bird vet - not someone that sees only 1-2 birds a month, somebody that sees a LOT of birds.
How did I get started on a lecture about bird health, anyway?