There are at least three dimensions here: Feels like imposter, is imposter, and cares. I'm not going to enumerate all 8 values since that's trivial, but realize my point is that conflating the first two dimensions is what makes the exercise intellectually empty. There are people who feel like imposters (or aren't), are imposters (or aren't), and still don't care about their ability to do their job.

I'm still quite skeptical, but even this simple conversation is far deeper than any discussion I've seen on the subject. I would never have bothered to think about the caring dimension if you hadn't mentioned it.