Working to failure is how you improve endurance in any form of exercise. The likes of a rotator cuff injury are usually caused by poor form or muscle imbalances, and while the former is definitely much more likely when you're tired, it's not the tiredness itself causing the injury. When you hit failure in a push-up you'll just fall onto the floor. Nothing should be pulled unless you've started using poor form to try and pump out extra reps, which is the issue with forcing them to do it for 30 mins(since they'll be hitting failure many times and their form will be AWFUL by the time they finish). So I agree in the sense that the punishment was extreme in the sense that the length of the exercise was far too long and completely impractical, but the assertion that exercising to failure is bad for you is simply wrong. You should always AIM for failure or as close as possible to it to improve.
No, I agree with you about failure. Exercising to failure isn't bad necessarily, but you have to have some idea of what you're doing and how to go about doing it the right way. Considering the circumstances I can easily see how it would be the wrong way to go for these guys. The kids aren't on a routine, they're being punished. If they were used to doing it, it wouldn't have the same effect and he'd probably have to come up with something else unpleasant. The father certainly doesn't look like he's into fitness himself, so maybe he doesn't know any better either.