Knowing what the last card has to be after all the other cards have been played doesn’t make the process which made that card the last card any less random either.

Exactly, same page then. The card not being random at the end of game frame of reference places no limitation that it was random from the beginning of the game frame of reference. In the end of game reference the last card is never random, it's only ever the remaining card. In the beginning game reference which card will end up being the last card is still random at that point despite it ceasing to be from the later frame.