While perhaps not "true" intelligence (whatever that is), with LLMs this can be emulated with a prompt:
> You have an innate curiosity to drive lifelong exploration and learning. ...
If the behavior of the system is indistinguishable from "true" intelligence, the distinction becomes a philosophical one.
I could maybe see chatbots storing everything you ever said in a vector database for future lookup, but that's just memory.
We are all, to some extent, a product of our environment (training data). I wasn't raised in that type of area, but does that mean my own intellectual curiosity is more innate? Or does it mean it is less innate? I could argue that both ways.
Innate traits such as curiosity & boredom are things that we are born with, not learnt. The reason evolution has selected for these innate traits is because there is a benefit (encouraging exploration and learning which help survival), but you don't need to be aware of the benefits to experience and act on boredom or curiosity.
Innate behaviors can certainly be reinforced, or suppressed to some degree, by experience.
Any true human-level (or even rat-level for that matter) AGI would need to have actual innate traits such as curiosity to drive lifelong exploration and learning. That seems a pretty minimal bar to meet to claim that something is AGI.
I suppose in context of an article about giving Claude a character (having it play a character) then we need to interpret "having a trait" as "playing a character having a trait", because it certainly is very different from actually having it.