What happened to the cultural intelligence hypothesis?

I read a bit more about the "cultural intelligence hypothesis" in academia recently. Here is a quote from 2007:

Humans have many cognitive skills not possessed by their nearest primate relatives. The cultural intelligence hypothesis argues that this is mainly due to a species-specific set of social-cognitive skills, emerging early in ontogeny, for participating and exchanging knowledge in cultural groups.

- http://science.sciencemag.org/content/317/5843/1360

IMO, something has gone wrong here. The cultural intelligence hypothesis should be a cultural counterpart to the social intelligence hypothesis - which argues that complex social lives led to big brains and advanced cognition over evolutionary time. The cultural intelligence hypothesis ought to be the cultural version: culture led to big brains and advanced intelligence over evolutionary time. It does so in many other papers on the topic.

I don't know how the term "cultural intelligence hypothesis" came to refer to such a watered-down hypothesis. The 2007 paper cited above is an early use of the term which is often cited by later work. It seems lamentable that the more interesting version of the hypothesis is getting diluted by this inferior version. Other researchers seem to have abandoned the term in favor of the Cultural Brain Hypothesis (2018).