Are you suggesting that the ability to model others or respond to nonverbal cues is innate, rather than learned?

Yes, I am not only suggesting but saying it explicitly (but see caveat below). Huge, obvious case in point: the autism spectrum. People on the spectrum (such as myself) have little to no ability to perceive nonverbal cues or (non-explicitly; again see caveat) model others.

Even for neurotypical (that is, non-autistic) people, there is a range of ability in this area.

I would definitely disagree, though proving it would be difficult. I suspect that it's a matter of internalizing the results of numerous actions and reactions in different situations. In my experience, it's often developed by people who travel lots or are otherwise exposed to tons of different people in a situation where being friendly and getting on their good side is very helpful. Some of them, pretty bad at socializing before they were in such a situation (and really gave it the necessary effort to learn).

Caveat to the above: I think these skills are innate in most people; that there is a range of ability, with the autism spectrum at one of that range and naturally charismatic, socially apt people on the other; but that the skills can be learned, with effort, as explicit skills.

For instance, autistic people can train themselves to recognize nonverbal cues and social signals; but this is not a matter of simply unconsciously perceiving the cues/signals/situations and just "knowing" their meaning, as it is for most people; rather it is a case of consciously paying attention and looking for things; and the meanings of these cues and signals must be looked up, researched, and memorized. In other words, a logic-based approach to compensate for lack of an intuitive ability.

It is probably also the case that neurotypicals who are not on the extreme positive end of the social ability spectrum, but do not lack the innate intuitive ability, can train their ability in the manner you mention. I would not know, of course, but it seems plausible enough, and consistent with what I've heard.