I don't really support HIT over any other method, but when I went on my universities sport science database, almost all the research studies comparing single versus multiple set training showed hardly any difference in strength gains. In Berger's study he concluded that 3 sets improved strength significantly better than 1 set training.
When I looked at the data though, the single set group (6 reps) improved by 25.5% over 12 weeks, and the multiple set group improved by 29.6%. 300% more volume, for 3% more results. The mean 1rm for 3 sets was 73.3kg versus 71.0kg, thats 2.3kg. 3 times more work to lift a bottle of milk difference?
I was taught HIT at my shitty personal training school and was pretty dogmatic about it, it definitely works, but I have recently changed training methods to see how they work. HIT did work for my clients. Most absolute beginners, and have gained a lot of strength, many doubled in 12 weeks. It's good if you don't have a lot of time to strength train. Keep an open mind to it if you have time strapped clients. Something is definitely better than nothing.
Nutrition wise, carbs make me feel poos. Maybe his theory is that all those carbs will spare the protein being used for energy. As far as I understand most universities still teach the typical high carb, low fat, medium protein diet.