@Ulthar - Nice to bump into another chemist too. I can tell by your post that you too have suffered through the agony of actually learning quantum mechanics.
This post has a zero probability of existing here --> <---but starts again here? Really, how did that happen? It must be a quantum tunnel!
Your question is valid and here is where you hit a huge split in chemistry. By "popular view" in chemistry I'm narrowing this down to the organic chemists, biochemists, and others who don't get to dealing with things quite as small. I myself am a polymer chemist which is like an organic chemist but even lazier with math as we do alot of averaging but then at the end of the work we have a nice physically existing object (a polymer). I got to admit one of my issues with quantum is I can see the entire subject being completely redone in a decade or so when we get actual experimental data on some of these things.