Do birds respond to petting, like cats and dogs do? Do they like being gently brushed against their heads? Does grooming in this sense exist in the avian world?
Many socialized birds do enjoy a gently scratching. The favorite places are the side of the neck and some birds enjoy under the wing.
Many parrots do groom each other, especially areas they cannot reach themselves, like the back of the neck and head. Scratching these areas closely mimics this grooming. An important part of the grooming is to clean away the 'plastic like' casing around a new feather as it emerges.
A bird will give clear indication when they like it, often dropping their head and fluffing the feathers around the head and neck. Start slowly and gently until your bird grows accustomed to it. Every bird is different, some LOVE it and others do not. It is highly dependent on the bond you have developed with the bird.
Most birds like being pet; however, first they must trust you. If you just got a bird and want to start bonding with, it my suggestion is to start petting it on the beak.
I have a Red Macaw and it loves the attention; however, I started by petting it on the beak and now after a couple of months, it asks for its petting time. Birds mostly enjoy if you pet them on their head, gently gliding your fingers against their feathers from back to front.
However, as they have already told you, some birds don't might not like that much attention.
From all the birds that I have had, I can tell you the most important thing to do is to respect their wishes. If they don't want to be pet, they will let you know. However, all animals love affection and if you forge a bond with it, it will ask for your attention frequently.
Hope this helps you.