I agree with a lot of what he says. Correct me if I'm wrong but he is basically saying if you get stronger in relatively low reps and low sets you will get bigger. Truth in that but also truth in that muscular endurance might play a bigger role in muscle size than pure strength. If it's pure strength that makes a muscle bigger why don't we all do our exercises in say sets of four and single reps (4 x 1)? That's a fast way to get stronger. Reference muscular endurance I am not talking about aerobic endurance but rather using my term of muscular endurance. Training with volume will increase muscular endurance and muscle size. The overwhelming majority of successful champs have used this method. Some might point out the failures too but that doesn't negate how many champs have used volume. I think ultimately both are important for muscle size. Getting stronger for low reps and getting stronger for endurance lifting. Guys that are use to lifting heavy for a low amount of sets are often shocked how hard it is to do their exercises for say 5 sets of 12 reps.
One thing is a fact. A work ethic often trumps every other factor except genetic predisposition.
100% agree with the bold written statement (the rest of your posting as well).
I remember a recent meta-study of Brad Schoenfeld, that shows a relation between volume and the rate of hypertrophy with a near optimal volume of >=9 sets per muscle/week.
Applying both methods (a strength phase and a 'pump' phase) in a periodization scheme might lead to better results on the long term, but keep in mind, not everyone will respond the same.