Gotcha, Slowbrew. My statement was a bit inartful - you are correct. We need to oxygenate (pre-fermented) wort to promote conditions for healthy liquid yeast or re-pitched dry yeast metabolization. My point is that some would be concerned with filtering both aspects of post boil - HSA (at high temps, admittedly, that is the "hot" in hot side aeration) and also in prematurely oxidizing wort that isn't fairly quickly inoculated with the yeast to consume the O2 before preliminary staling precursors set up (really only applicable in long-delayed pitching that is practiced by some - though no chill has its adherents and seems to work well for those who give it a try with an Aussies cube or the like).
With finished beer, O2 is to be avoided as much as possible, of course, hence the gentle racking mentioned. I think we are in agreement - Cheers.