Im talking for BBing, not for sports or strength. I really dont want to get into a pissing match for you. Some people can grow on 1x/wk training (per bodypart). Most people make very little or no progress at all on those programs. Look at anyone in your gym who trains that way. 90% will look exactly the same this time next year, and this time 5 years from now, and 10 years, and so on. They read the programs in the magazines that the pros supposedly use and make zero progress. Its not about how hard you train (what people mistakenly call 'intensity') or making yourself as tender as a filet mignon from the soreness.
Science shows that you can train a muscle within 48 hours of working out. Doing this will produce much better results. 3x/wk might be too much for some. I like 3x/wk when bulking (Im actually at about 3-4x right now for dieting). Others, like Hogg or in AnimalMass's DFHT program prefer 2x/wk.
When someone trains once per week, they are already in the deconditioning phase of the recovery/growth process. They are taking 1 step forward and 1 step back. Or 5 steps forward and 4 back. By training with a greater frequency, you take 5 steps forward, and maybe 1 back.
As for the "take a day off" statement from earlier, the guy does need to take at least a day off. Id like to know when the last time was that he stayed out of the gym completely for a week. It wouldnt surprise me if its been months and months on end. A week, or even two, out of the gym would do his body wonders. Plus, when he returns he'll be back on the road to progress.