It sounds like you may be demanding more from AGI that we do of humans. AGI is a mushy concept, not a hard requirement. "Any task" is definitely not required for a low functioning AGI, just as it's not a requirement for a low functioning human, who still easily fits the definition of an intelligent being.
For each human being having GI there are many tasks that person won't be able to perform. For example proving math theorems, doing research in physics, writing a poem, etc. Specyfic AGI could have its limitations as well.
AGI isn't really explicitly defined (it wouldn't be a problem if it was) but it's essentially an artificial version of the "general" intelligence that humans have, aka we can do and learn many things we were not programmed or trained by evolution to do