This author seems disagrees with you:

"Heritability does not indicate what proportion of a trait is determined by genes and what proportion is determined by environment. So, a heritability of 0.7 does not mean that a trait is 70% caused by genetic factors; it means that 70% of the variability in the trait in a population is due to genetic differences among people."

https://medlineplus.gov/genetics/understanding/inheritance/h...