I'm not real sure what your theory is, you do use the term unique and defining complex would help, Sperm whales have the largest and most complex brains we know of, elephants are also unique in both brain size, complexity not to mention behaviors. A mormyrid (an electrical blind fish) has a larger brain to body ratio than humans not to mention complex behaviors.
Unique could also use some definition, both whales and elephants are known to have language and are able to share complex information. I would argue cephalopods are smarter than we are in significant ways. Corvids as you mention are capable of some amazing behaviors and communication interaction. They are able to communicate highly complex ideas between each other not to mention read human behavior better than we can all with a very small brain.
I am questioning your neutrality on this idea, to be honest I'm not sure a human can be neutral when trying to judge or compare non human intelligence with human intelligence. We have a natural bias, human chauvinism is written into our own behaviors.
So far you have not listed a single way humans are unique or superior to other animals... or at the very least listed a way we can know this...