Specifically, a number of IQ tests have been designed with the intention that they would not produce a positive manifold (which would I think to at least some extent imply not agreeing with existing tests). Instead they end up producing a positive manifold and mostly agreeing with existing tests.

Coincidentally, I just came across this, probably already well-known and discussed on LW, which includes claims that rationality and intelligence "often have very little to do with each other", and that "it is as malleable as intelligence and possibly much more so". So there's a clearly cognitive skill (rationality) claimed to be distinct from and not closely correlated with g.

Has evidence yet emerged to judge these claims? The article is less than a year old and is about the start of a 3-year project, so perhaps none yet.