This whole idea of empty space within atoms is just nonsense using English grammar as a substitute for physics. It's a meaningless statement either way until you define the terms specifically enough. And by doing that, you can choose whatever answer you want. "occupied to the point where nothing more can be added" isn't specific enough because you can still add a lot of photons to a "filled" glass of water, so that means it's not filled by that definition even though it is by common sense. It just shows the irrelevance of everyday words and concepts at the subatomic scale.

Even a neutron star is practically invisible to neutrinos which can easily pass through it despite it's being "filled" with neutrons.