You're absolutely right about that. After a while, a bird almost seems to think it's human if it interacts enough with you. I had a cockatiel when I was younger that could fly, but he seldom did. If he wanted to get from the floor to the top of the couch, he'd crawl all the way up the side until he got where he wanted. Sometimes it was really funny to watch. He liked to fly around outside during the sumnmer, but wouldn't stay out long because other birds wanted to pick on him.
Birds, especially large ones like African Greys, and cockatoos are very time-consuming animals to have. To keep them happy and healthy, you really have to spend a lot of time with them. They also can live longer than you do, so it's important to make provisions in your will for them. Winston Churchill's parrot is still alive and kicking at 112 years of age, and still says "F**k Hitler" in Winston Churchill's voice.
Did you ever hear the story about Andrew Jackson's parrot ? In his will he stipulated that the parrot should attend his funeral, but the bird proved to be so foul-mouthed and loud that they had to remove partway thru.