No, no, no! Stockpiling is not a solution to a bottleneck! In the grand scheme of things, having a couple weeks of extra inventory on hand will not help you weather a 100 year storm. But it will increase waste - inventory that you have to throw away when there are defects or when they become obsolete. Imagine trying to predict the run on lumber, and the solution was to have kept a bunch of lumber sitting in yards rot…
That's not really what he's saying. It's not about a single company, it's about the whole economy. When every company is running JIT, a small temporary supply disruption anywhere can bubble and propagate through the whole chain, becoming a huge disaster. It's like a traffic jam; when a highway is running right at capacity it only takes one person hitting the brakes to turn the whole thing into a parking lot. Except it's worse than a linear highway because the economy has many backlinks where companies early in the chain rely on companies later in the chain, causing feedback loops. Whereas if there was slack in the system then the relatively small initial shock wouldn't propagate.