If you read the section on "The Paradox" in the article, it's basically using a simplifying geometric assumption to divide the universe into concentric shells, each of which contributes the same intensity of light to the observer. If space is sparse enough that any light reaches us from shell N+1, then you'll get the same amount of light from every shell, and so you'd have a fully-saturated bright sky.

So there are possible infinite/steady-state universes universes (very dense, lots of dust) where you don't see shell N+1. But since we can see stars from shell N+1 and other shells, we know that we don't live in that universe. Therefore our universe isn't a steady-state / infinite time one.