This might be true in many cases, but not all. I'll give a personal example - when I was a runner, I did my mileage at various paces, most of which I had no clue about. When I read a book, Running Formula by Dr. Jack Daniels, it was the addition of very specific things like tempo runs and adjusting the pace of my easy runs that caused me to improve without any change in overall volume.
Often the right answer is, "It depends." You did say "the greatest" determinant, and not the only, so I'll give you that.
-S-