I really don't see the point of a discussion on what is the ONE most important thing. I only care about what is optimal and real world.
You need to look beyond the acute post workout window and look at big picture. What I mean by this is protein synthesis rates can be elevated for up to 36hours after training and glycogen synthesis rates can be elevated for up to 24hours post training. So the big point I am making is that as long as an optimal amount of carbs and protein are consumed within that time window, you should optimize recovery. This has even been shown to be true regardless of the source of carbohydrate or protein. For the grand majority of gym goers this will hold true.
Now we have no research on a precontest BBer doing multiple training sessions a day, in a major caloric deficit and taking "supplements". So this is when the detail will matter and the acute studies come into play to try and make the smallest difference to enhance recovery.
I am sorry to say the initial post is incorrect about how nutrition metabolism occurs. Many think it terms of one process must finish before another starts. But all process (protein synthesis and breakdown, glucose oxidation and glycogen storage, etc) occur simultaneously. What changes is some process elevate and some decrease, then you are left with a net result. I have studied the shit out of nutrition metabolism and it is very complicated.