This is a great question, which strikes at the core of the history of European folklore studies. Early scholars of oral tradition were diffusionists - along with many scholars of the other disciplines of the humanities. When they found examples of frame tales from the literature of the early, impressive Indian civilization, it was easy to imagine that this device originated there and then spread to the more "primitive" outreaches of Europe. Coincidentally, some early Indian examples of folktales that appeared in European collections suggested that the diffusion of the frame device brought with it some stories.

Did this diffusion occur - both for the frame device and some folktales? Perhaps, but that doesn't mean that others did not independently employ the frame mechanism as you suggest. I suspect there was a little of both.

Stith Thompson in his classic essay, "The Folktale" deals with this. And you can look at the two excellent collections of essays gathered and edited by Alan Dundes.