All the article says is that "empty" isn't enough information. If "empty" means "I can put electrons in there", then it takes more binding energy to pack more

All the article says is that "empty" isn't enough information. If "empty" means "I can put electrons in there", then it takes more binding energy to pack more electrons into the same space. If you want to pack more electrons in, you have to squeeze harder. Example: you can confine an electron to a tiny part of an atom (electrons in inner shells of heavy atoms, for example) but those electrons are very tightly bound (held in by very high ionization energies). Or the "emptiness" of an atom could be measured using neutral particles, which don't interact with the electrons at all and sail right through as if the electrons were empty space. For what it's worth this is normal sophomore physics. There's no way to just dismiss it. But there's also no way to claim it's less than a hundred years old.