There's no contradiction, really.
I can't speak for others, but my chest workout doesn't really hit the triceps intensely. Sure, the triceps work, but they aren't incredibly fatigued by the end of the workout even though my chest is trashed. I train them the day after chest, and they are fresh as fuck.
Similarly, my back workouts will make my biceps a bit tired by the end of the workout but they aren't really stressed to the point that I would say I had "trained" them. Which is why I have no problem training bis the day BEFORE my back: When I'm rowing or doing pullups, it is my BACK that is doing almost all of the work.
Et cetera, et cetera...