Correcting other people's children

Yesterday a friend and I were talking about the taboo many people seem to have about correcting other people's children when they are misbehaving. Then this morning, I found this article from the Today Show about how to deal with other people's misbehaving/annoying children. In it the parenting "expert" completely accepts the idea that one should never correct someone else's child even in the face of bullying or extreme rudeness (she mentions a child burping in your face). Can someone please explain the thinking behind this taboo to me? Now, I wouldn't yell at someone else's child or interject myself into the life of some random obnoxious child I saw while walking down the street. However, I see nothing wrong with telling a child who is operating in your common space, "please stop doing that. You're going to hurt yourself/it's very rude/you make other people feel bad" or whatever is appropriate. Occasionally, my children are corrected by another adult and they know that they need to deal with that and not give people cause to correct them. Of course I would never be abusive towards a child and would not tolerate another person treating my child in an abusive manner, but simply correcting poor/dangerous behavior seems perfectly fine to me. Every time this topic comes up, I feel like I must be missing something as I just cannot understand why stepping in to speak to a child who is out of hand should be a problem.
Many of us (or at least our parents) remember a time when if you misbehaved out in public, not only would any adult present reprimand you, but they would likely make sure your mother knew about it by the time you made it home so she could deal with you as well. I think that the difference between those times and today demonstrates a change which parents neglect to take seriously at their (and their children's) own peril. Once upon a time, you could be a fairly negligent parent, not devoting much energy to supervising or disciplining your children and feel fairly comfortable that your kids would turn out basically OK. That was because while you might not be there with your kids, other adults were watching and correcting problem behaviors. Your children simply could not move through the world in most places without having societal norms enforced on them. Having other parents and the community re-enforcing proper behavior and norms assisted parents in raising good kids. I think too many parents fail to realize that since this mechanism is no longer in place, they are wholly responsible for their child's development. Too many parents act as if they can still send their kids out into the world and have them be OK. It's not just that we live in a more dangerous world - the reality is that crime has dropped very dramatically in the last 20-30 years. Statistically speaking, we're much safer today. However, what's missing is any re-enforcement from others our children will meet as they move through the world of the sorts of good behavior and proper character development we're teaching our kids. Instead of living in a world which helps us as we raise our kids, we must equip our kids to defend themselves against the world. It seems to me that this cultural taboo we have about correcting other people's children simply feeds into this problem and makes raising good kids that much harder.