Hi Rich,
I am not familiar with this theory and have not read any studies to confirm it, so I can't say for sure. Now, it is true that there's a central nervous system component of strength. That is, the brain sends signals down the CNS to recruit muscle fibers. The more you train, the more you "wake up" the CNS to recruit more fibers. People get stronger in the first few weeks of a strength training program without significant growth in muscle because they are waking up the CNS, that is, recruiting more fibers. Studies that measure electrical activity of muscle after weight lifting programs show significant improvements in just a few weeks in people of all ages due to a CNS effect. You read studies of elderly people getting 100% stronger as a result of lifting due to increases in CNS activity and not hypertrophy.
In addition to the CNS improvements in strength, muscles also grow because you make microscopic tears in the fibers when you lift, and then they recover and you gain mass and strength. The muscle mass growth occurs while you rest, not when you train, and that's why it's recommended that you leave some downtime between sessions for rest and recovery. People who lift weights every day may be alternating muscle groups so as not to work the same groups each day to leave time for rest and recovery. This is especially important if you work to fatigue with every set.
Importantly, progressive overload is the principle that governs strength and mass development. That is, as the muscles accommodate to a certain weight and training volume, they need more stimulus to gain more benefit. No matter what regimen of resistance exercise you use, this principle is almost certainly relevant.
As for this theory you're describing, there was a recent study that showed that you don't have to work to fatigue with every set to get stronger, and that may be what this new theory is using as a foundation. It's not that difficult to believe since you are tapping into the CNS along with some hypertrophy for strength development, but since you're not working to fatigue or failure, the recovery time will be less.
The thing about only 30 seconds of rest in between sets is that it sounds like circuit training, and CT is a well-known style of lifting where you move quickly between exercises, keeping your heart rate elevated the entire time. This is what they do at Curves. CT is a proven way to train and will develop both strength and aerobic fitness, although not as much as a dedicated workout of either. But it's good work and I recommend it to people who might want a change of pace, or just want to combine the two and save some time.
A problem I see with this theory is the potential for overuse which can lead to tendinitis or bursitis. 100 reps in a very short period of time can be demanding, especially for novices. I suggest caution and building up slowly if one were going to do it. Another potential problem, even if the load is submaximal, is working the same muscles every day, and so again I recommend caution.
Overall, I don't see professional athletes who depend on maximum strength, or bodybuilders who depend on maximum mass development, using this training method successfully. The stimulus won't be great enough. For recreational lifters, I don't see a problem with experimenting with it, with the exception of the potential for overuse as I stated, and so one would need to build up to so many reps in such a short period of time, and even then, pay attention to signs of overtraining, which would be loss of strength, chronic aches or pain or soreness, and stop if these occur. If I were going to recommend it, I would recommend starting with only 2 or 3 days a week with a day or two of rest in between to accommodate to the "circuit training" type of workout that this is.
If you post a link to what you've been reading I'd be happy to have a look.
Take care, Rich