One of the funniest stories I think I've ever read was about parrot speech that took place at a parrot rescue operation. The birds had all been previously owned by people who didn't realize they're too smart to be a pet, in the traditional sense. They're not domesticated, and the best you can hope for is taming them. Unlike dogs or cats, birds have egos as big as all outdoors and don't take kindly to any kind of disrespect.
The author of the article visited this sanctuary and related how the birds would scream "hi, how are you" when she came through the door, but when she moved closer to their cages, they'd sidle up to her and whisper, "fuck off"! You can surmise that they were imitating their prior owner, who thought they could get away with swearing at their bird, if they moved close to the cage and whispered.
I looked after an African Gray parrot, of a friend, who only imitated swearing and anything that was said with passion. They have a boat and the close quarters enabled the bird to hear them making out. He would do a medley of "alright, that's great. Oh Baby. Then the obligatory panting and sighing, followed by a satisfied series of grunts, followed by a low whistle.
African Greys are the best talkers and imitators. The interesting thing about their ability to imitate, is, they seem not to use their talents for mimicry, in the wild. Their wide range of sounds, and ability to manipulate their throats, is understood to be mainly for communication within their own species. They likely have language and use it with each other. Nature wouldn't devote a large part of the brain to this feature and not have a use for it. The reason they talk and imitate humans, in captivity, is based on their strong desire to communicate with their own species. If they're not socialized with other birds at a critical juncture f their young lives, they identify with people, not birds.
It's also been revealed through work with grey parrots that if they have a strong attachment to their owner, the owner can be reading a magazine or picture book in another room, and the parrot can do a running commentary about the pictures she's looking at, without seeing the pics himself.
I agree with the poster that other animals likely convey a heck of a lot of detailed information, that sounds like gibberish, and mere random noise to us. Parrots may not actually be unique in their ability to communicate their thoughts. It may only be their desire, as pets, to communicate with us, and their ability to imitate our form of speech that separates them from other animals.
The study of animal communication, through the study of parrots will do much more than illuminate how intelligent animals are. It will help us understand the realm of psychic communication, therefore, give us a little more insight into ourselves.