(Hence religion.) You are of course right about the basics. I'd take it even further and suggest that our very sense of self is based on our ability to identify with and replicate those we see around us at an early age. Even as an adult I see a tendency within myself to take on the characteristics of other people. Whether they are acquaintances or just characters in a movie. But I still think that the basic mechanism requires an ability to create models. A child sees its parents and tries to make sense of their actions. And it eventually begins to recognize similarities in its own actions and desires and begins to build a model of the self. From then on the self becomes the reference point to which every other model becomes oriented, transforming simple awareness into conscious awareness.
It'd be interesting to define what we're meaning by 'model' here. I'm taking that to mean a definition of larger patterns and insights that help dictate behaviour, or just integrated solutions that make behaviour more efficient.
I'm of the opinion, personally, that the vast majority of people are followers of their culture, whose behaviour is dictated by what allows them to maintain the support of their social circle. Very few, if any, concepts dictate their everyday lives, beyond those that are already present in their preexisting culture. Many of us may build a model of the self to the extent that we understand a few key characteristics (what we're good at, what we're not good at), but beyond that I'm doubtful that actual, day-to-day cognition is really doing much beyond making sure we're fed and warm.
As intellectual ability expands what we're seeing is heightened pattern recognition, which increases the extent that new solutions (concepts) are integrated into the psyche. In a certain sense, people who are more intelligent are fundamentally more creative, and so more free to carry out a wider range of behaviour. These people learn to look beyond their own culture and form a more unique identity.