Do talking birds understand what they are saying?

Research has shown that certain parrot species such as the African Grey , do understand what they are saying and even use their wide vocabulary at appropriate times. But until more research can be conducted, most talking birds mimic the words and sounds they hear. I wonder if my cockateil knows what he's doing because when someone comes into the house, he always gives this big wolf whistle. They could be a lot smarter than we give them credit for.