Isn't heritability more important to genic capture than just genetic variance?

Rowe & Houle (1996) give two criteria for the selection of costly female choice:

1. Condition dependence of sexually selected traits


2. High genetic variance in condition

Regarding heritability, they wrote,

comparisons based on heritability are misleading, as Fisher's fundamental theorem of natural selection shows that the response of fitness to selection depends only on the additive genetic variance, and not on other components of variance.

However, the magnitude of environmental variance should matter for the selection of female choice for sexually selected traits, since the more environmental variance means the less likely offspring of fitter males will be fitter themselves and the less likely females should be to incur costs to mate with fitter males. Am I not correct? Is this an oversight on their part?