This is the kind of religious attention to rigor that undergraduates benefit from, but that researchers couldn’t care less about. It’s the analogous “well actually” guy for mathematics. Part of graduate school training is to teach you to distinguish between important and unimportant issues, and I think the empty graph is a clearly unimportant issue. And even the authors admit this at the end, so I can only infer the article is something of a joke.
Sometimes rigor can unveil a important point hidden in a seemingly unimportant stuff. It’s just a LOT less likely to do so. If you have the free time though might as well peek.