OP, you didn't have to mention not having children yet--your post has so many dead giveaways that you're not a parent.
For your original question...as others have mentioned, we parent the same way at Disney as we do at home. And ya know what? Not all techniques work all the time on all kids. It may be a minor miracle that the mom was able to calm the child down in this case...it's just as likely that she wouldn't have been able to, or that her intervention would make the child even more upset. The only guarantee in parenting is that no matter what you do, you'll be judged for it. Just a few weeks ago, on this board, my parenting was brought into question because I dared to admit that I wouldn't let myself be manipulated by my then 3 year old at Disney. I was told that my parenting was likely to blame for my 3 year old crying at Disney, or ever, really. So that was awesome and also a reminder that every time you take your child out in public, there is going to be some know-it-all out there who will be judging you, your child, and your entire family based on a few minutes' observation.
Everybody has a bad day. Everybody gets crabby. Three year olds are unpredictable at best, and unfortunately, they don't come with an owner's manual. There is added pressure at Disney, because you're in a public place, everyone has paid a lot to be there, and nobody wants their vacation infringed on by a misbehaving child. So, you do the best you can.
Our kids are currently (almost) 5 and 8. We are finally to the point where they are both mostly rational and well-behaved most of the time. I really can't imagine a time at Disney where we'd have to really discipline our kids at the ages they are now. They're both pretty good, agreeable kids, they're especially well-behaved at Disney because we're having so much fun, and we've learned to keep a constant supply of snacks with us when we're in the parks, because for our kids, any general crabbiness really seems to stem from being hungry. At Disney, having them eat something pretty much every 60 to 90 minutes is really key to keeping them happy.