Think of a cake. Is a cake determined by its ingredients or by its preparation (mixing, baking, etc)? It's a meaningless question. The cake is determined by both.
Now think of two cakes. In principal, we can now begin to talk about the causes of their differences. For example, if they had identical ingredients but were prepared differently, then we could say that the differences in the resulting cakes were due to different preparation.
Humans are baked cakes. Quantitative genetics is a field which tries to estimate to which extend differences between organisms are due to genetic factors. Learned behaviors are consistently found to be heritable in quantitative genetics studies. For example, adult vocabulary size is substantially heritable. It is not that the words are literally transmitted to the offspring, but rather genes that influence the cognitive abilities, interests and personality of the individual. That vocabulary size is "heritable" means that a substantial portion of the differences between individuals' vocabulary sizes are due to genetic differences (although by no means only due to genetic differences).
In short, what I'm trying to get at, is that you can only talk about the relative contributions of genes and environment if you're talking about it in the context of differences between individuals. In that case, yes, learned behaviors have an innate component.