I thought that Piketty released or references sources for the underlying data supporting his work from "Capital..." so why are you considering it not necessarily testable? I don't understand what you mean by that phrase.
For example, colonialism, which Picketty and Acemoglu base a lot of their work on, would be hard to reimplement for experimentation. Hence the debate. The data and conclusions are interesting and compelling, but not yet decisive.