“There’s not enough water on earth to make that much ice.”
Actually there is... Much of it is in the atmosphere at all times.
You make a good point, that there’s a LOT of water as vapor in the atmosphere. There’s a lot more than I was aware of. If it all fell at once, it would add a 1.7 mile thick layer of water, and even more than that if you take into account mountain peaks. That’s still not the “several miles” of ice stated in the article.
Another point is that there would be substantial sublimation of the ice due to zero relative humidity, so the earth would never have all of the atmospheric water on the surface as ice.