I do experience inner speech when I do (which is often), but it is very clear that this narrative thinking is not my core thinking thinking; rather, I think in non-linguistic concepts and then can (slowly!) translate thought to language for myself or to others.
Or so it seems to me. It's possible for internal qualia like that to be wrong (there's no lack of such wrongness discovered by cognitive science).
Nonetheless, the language-required-for-thought hypothesis has thus struck me as quite amusing. I have noted over the years the fMRI papers and accounts of stroke symptoms and so on that seem anecdotally inconsistent with the language-required-for-thought idea. But then it was never my impression that neuroscientists took that idea terribly seriously to begin with--wasn't it was mostly a philosopher and linguist thing? This is more easily explicable as people who love to use and study language in complex ways hoping that they are embracing cognition itself than a careful analysis of the possibilities and the judgment that language is a prerequisite for thought.