I think you're missing the point. First, he actually started the video saying move speed was one of the stat that was fine fluctuating because it's an obvious one : faster champions feel faster, slower champions feel slower.
Second, his point wasn't "Lucian and Vayne should have the same overall tankiness of whatever the decided line for ADC is" but rather that if Lucian is to be more durable than Vayne (which everyone should agree on as he doesn't have stealth and CC), that them having similar armor stats but having a higher difference in HP would make it much cleaner and easier to balance.
I'm not sure about your Caitlyn example though. If anything, she should be weak to Magic Damage as a form of counterplay. But the thing is, as Phreak mentioned, while there's plenty of mages that can waveclear, there's definitely a few AD champions that can do the same now. And in that case, there's no reason why she should be more durable to Oriana's W rather than a Sivir Q. Rather, it'd be a lot simpler to balance if her total HP and regen were on the lower spectrum in order to force her to pay (or slightly higher so she can deal with it, in your example).
Basically, the state of the game has changed to where poke, AoE and single-target focused damage all come in various forms of Physical, Magical, and sometimes, True damage. There's no reason for Sion to be drastically more vulnerable to Magic Damage than Maokai as neither were designed to be particulary better at either. Rather, if Sion is meant to have lower resistances because of his HP stacking, then that should be shown across both stats.