'Wouldn't the relatively cool temperature of the wort actually increase the solubility of the oxygen, and so reduce the need for vigorous mixing?'
For sure. Looking at those revision notes, I think they are probably trying to emphasize that it's important, regardless of when oxygenation occurs, to provide some aid to the oxygen in dissolving; it's one of the very few advantages of aerating hot that the pressure and (more importantly) the turbulent flow of the heat exchanger make gas dissolution, as a percentage of total gas injected, very high.
Even with the increased solubility at lower temperatures, if you do not provide some sort of restriction, dispersion or turbulence between the fermenter and the oxygenation point, a lot of that oxygen can arrive at the fermenter not fully dissolved, thus being wastefully added but also breaking out and causing foaming in the fermenter (which can strip volatiles and foam-positives out). This is especially likely to happen early in knockout when the liquid level in the fermenter is low and therefore provides little hydrostatic back-pressure. In my experience it's incredibly common to see even larger more established (pro) brewers practicing aeration so vigorous that most of the gas injected just comes right out before it has any chance to dissolve. If you can see enormous bubbles in a sight-glass, it's a pretty good guess that that oxygen isn't getting dissolved!
I will say I've studied quite a bit through the IBD and I find their information great in general, though they can be a bit obtuse at times.
Good luck with the exam!