"Heritable" definitely means genetic when used in a technical rather than a casual sense, though. Studies control for environment by looking at, for example, identical twins adopted by different families.
Heritability refers to trait variation due to genetic variation within a population.
This is different than the amount genetics actually contributes to a trait.
While you are controlling for environmental factors in heritability studies you are still referring to a specific population. It can be the case that two identical genotypes across two different populations show two different phenotypes.