Personally I've found very little of Parrelli's system to be usefuil with my horses. In one case it would have been rather dangerous....and that was with one of the easiest horses I ever trained. Even Parrelli doesn't show you the problems he's had with some horses and some of the methodes he's used to force a horse to do things that actually go against what he promotes. If it doesn't make his system look wonderful you don't get to see it . But none of them will show you the problems or their failures.
Like most of the people who are selling a product they have to be in lock stepped with what they promote. It wouldn't be practical for them to admit that their way isn't always right or always work. Would be a bit like a driving instructor who admits that what they teach might not be right. They probably wouldn't be in business long.
I'd take the time to read that other thread. There's a lot of different inputs.
Training your horse isn't about following someone else's "system". It's about using what gives you the best results. Knowledge of horses in general, the horse you're training in specific and a lot of common sense will be the most useful things you have for training a horse. If you need ideas I'd look at what the different promoters have out there. Use what will work best with your horse, but I'd never say you should become a follower of any of them. And remember that you can have ideas and insights that might work better for you than what they promote. They don't know your horse. You do.