It's not anthropomorphism, it's just life.
The exploring of an environment, learning and surviving is not unique to humans, but all life on this planet.
Sure, some of us may not see them (our alive brothers and sisters on this planet) as "intelligent", but undeniably their learned, and hereditary behaviors (learned through evolution, I guess), are very intelligent, especially for survival, and are tethered to the real world. They are all part of an intelligence which we all share.
They are (these behaviors), in fact, from a certain point of view -- reflections of the real world, or models of it. In a way that is even closer than language, or at least, orthogonal. We need that orthogonal source of real-world data (which is even more enriched with reality-info than language is), to bootstrap these AIs to a higher level of utility. :) hahaha :)
Regarding your point on degrees of fidelity with reality, the way I explain that is that they (OpenAI et al, or the AI models) have extracted world-information from semantic mining of enormous data. That's good, but only up to a point, as we see.
I think we need real world experience to get the rest of the way. Or, put it differently, to make it a helluva lot easier to get that juicy world info haha! :)
I don't think we to "prove" it. It's not math. It's a blackbox. We just have to try it and see. :)