I believe it's a mixed bag, or at the very least not a clear answer when it comes to innate talent. Almost every person is capable of producing art, as art is simply the creation and display of human emotion, regardless if it is perceived as good or not. Secondly, for what is typically considered good or aesthetic, I do believe some people have more innate talent than others, but of course many skills can come with practice and learning.
The role of an artist can definitely change with culture, especially through avenues when the artist is commissioned.