I don't think it is that...it is just that there is a certain TYPE of intelligence that we consider a basic tenet of human rationality...and up to recently, it has not been shown to be present in non-primates.
There are a lot of people who can agree that intelligence can be measured in a variety of ways, and while certain South Pacific aboriginal peoples may not have mathematical intelligence that would have stood them in good stead amongst the people who were involved in the Manhattan Project, the people in the Manhattan Project for the most part would have been very hard pressed to survive in the jungles of New Guinea with no food and water, where the natives would be able to do it quite handily. (NOTE: THIS IS NOT CULTURAL RELATIVISM I HAVE JUST DEFINED!)
If that "human" characteristic is there in animals, researchers have not been able to find a way to allow animals to demonstrate it for us, confirming they have it as well as us.
Now, I am not an animal behavoirist, and I do not play one on television, so take this with a grain of salt. But it has been my impression that mathematical skill is the domain of humans. That is, some higher level animals may be able to count, but it has not been demonstrated that they can take two counts and combine them and assign a numerical representation for a sum.
Sounds to me like this "Alex" is getting kind of close to that.
You bring up an interesting perspective. Sure, animals of all kinds have intelligence. Some even more intelligent than humans. But once we've used our intelligence to figure something out, we have the capacity to share that information to others. It's that capacity to share and build upon what we've deduced through our use intelligence that separates us from animals. Mathematics is one good example. Alex the Parrot won't be teaching his wild kin what he has learned. Every generation of parrots or octupi must rediscover what the past generation has. And even then, that information will not be disseminated to others of their species effectively.