That they didn’t break down the bird owners between parrots and canaries/finches was a major oversight - while some canary/finch owners do let their birds out and handle them, parrots (even budgies) tend to interact far more with human keepers than finches and canaries do.
Some parrots are out of their cage all the time and interact quite well with the family, like potty-trained 3-d dogs.
It is harder to take them outside for a walk though (although there are bird leashes). This sort of limits the outdoor social interaction that dogs confer.
and yes, some smaller birds are treated more like fish that a member of the family.