Nobody is claiming they aren't correlated. The question is: how strong is the correlation? The OP seems to insinuate they are extremely correlated on account that it is the sole consideration in the comment.
Like so many strong claims made online, it's an overly simplified mental model for something that is much more complex in reality. Like you said, we need more information before making strong claims.
I don’t think COLA matters all that much. The reason SV pays such high salaries reflects the underlying higher productivity of those engineers. The fact that much of that income goes to landlords in the Bay Area is orthogonal to the underlying quality of the engineers.