Isn’t that also wrong? From what I remember it’s the blue wavelengths of visible light that are scattered and make us perceive the sky as blue. UV may well be scattered too but we can’t see that, right? Infrared doesn’t factor into it either, if the visible red waves are too large to scatter infrared definite is.

Yes, that's what it's saying: "they scatter away the blue ones, which then bounces off the molecules and reaches our eyes".