Parrots don't have webbing on their feet... but a hooked beak? Do you know if only the very end is hooked, but is otherwise straight?
Like this for example?
Those are cormorants... there's also frigates?
YouTube - Greater frigate bird display
I don't kow if you have any cormorants, but my best guess right now would be a frigate...
As for wild birds not minding humans... either the birds just don't know any better or were never taught that humans were dangerous (or rather grew up in a community that has no predators) thus yes it may be possible for a wild bird to go up to a human. Some birds that may have been taught to stay away from humans can learn to depend on them too.