(You seem to have put your comments in the quote-block as well as the thing actually being quoted.)
Since immediately after the bit you quote OP said:
No. A perfect fit would only mean that, across a population, a single number would describe how people do on tests (except for the “noise”). It does not mean that number causes test performance to be correlated.
it doesn’t seem to me necessary to inform them that “determines” implies causation or that factor analysis doesn’t identify what causes what.
(Entirely unfairly, I’m amused by the fact that you write ‘”Determines” is a causal word’ and then in the very next sentence use the word “determine” in a non-causal way. Unfairly because all that’s happening is that “determine” means multiple things, and OP’s usage does indeed seem to have been causal. But it may be worth noting that if the model were perfect, then indeed g would “determine how good we are at thinking” in the same sense as that in which factor analysis doesn’t “determine causality for you” but one might have imagined it doing so.)
(You seem to have put your comments in the quote-block as well as the thing actually being quoted.)
Since immediately after the bit you quote OP said:
it doesn’t seem to me necessary to inform them that “determines” implies causation or that factor analysis doesn’t identify what causes what.
(Entirely unfairly, I’m amused by the fact that you write ‘”Determines” is a causal word’ and then in the very next sentence use the word “determine” in a non-causal way. Unfairly because all that’s happening is that “determine” means multiple things, and OP’s usage does indeed seem to have been causal. But it may be worth noting that if the model were perfect, then indeed g would “determine how good we are at thinking” in the same sense as that in which factor analysis doesn’t “determine causality for you” but one might have imagined it doing so.)