Well, we did a lesson already. No crying, no whining, no fussing, no screaming, no begging... my son was just total giggles most of the time. And yes, she took him under water about 9 times. Nothing came by surprise, she explained every step (told him to close his mouth, etc). I think this is going to fit our family just fine. Remember, every child is different. Individual temperments will handle various styles of teaching differently.
That said, I can see how some people would not be comfortable with it. Letting children go under water is really scary for some people. And the firm, no-nonsense tone of the lessons as well as the short duration could easily be a turn-off. I'm not sure I would want to do it with a tiny infant who doesn't understand language and can't follow directions. The cost is prohibitive for many people. And I really don't think this method is the best way to introduce pools and swimming.
To dejagerw: when I said I want my son to swim correctly, I meant that I want him to swim, not float around with floaties. I don't care exactly how he swims (dog paddling is fine) and I don't care how far he can do it. I don't expect him to do the crawl or breaststroke perfetly at 2.5 years old. But I'm also well aware that kids can learn to swim at young ages. I learned so young that I can't remember ever not knowing how to swim. My son is old enough to learn to swim a few feet and grab a wall. So that's what he's going to learn to do.