It seems that my use of the word "parenting" has caused a little *ahem* disagreement among a few people. I wasn't really asking about "parenting" a stranger's child as much as how to deal with misbehaving children. I personally don't think basic rules of civilized society are only to be taught to children by their parents - though it is nice when parents make the effort. I would say it falls under the parents job description, but I don't think a stranger is overstepping their bounds by reminding a child when they interact with them.
Of course parenting is for parents - hence the name. But I would suggest that while only parents (or guardians to be PC I guess) can parent (if you define parenting as discipline/control/ethically guide etc.), a child can learn from anyone.
IMHO that is where the idea or perhaps the real spirit of "it takes a village" comes from - a child learns how to get along in the big outside world by going out in it and interacting with the other people they have to share it with.
I understand where you are coming from and agree that children can and should learn from everyone. But, it may be a small distinction, but it is a distinction. A stranger is overstepping when they choose to teach manners to a child that is neither their own (or they are responsibile for) or is not directly interferring/affecting their or their children's lives.
For instance, I would tell a child not to shove on the slide, run out in traffic, not to throw things, or to be careful if they accidently bumb into me. If it's safety related, or interfering with me and/or my child, then it is my place to say something. I would treat an adult the same.
But, I would not tell a random child not to pick their nose, chew with their mouth closed, keep their elbows off the table, share their toys, pull up their pants, or stay near their parents in a crowded shopping center....all things that I would and do tell my own daughter every day. Just like I don't tell adults not to talk on their cell phones when checking out, not to cut in lines that I'm not in, not to check emails during meetings I'm not running, to wear properly fitting clothes or any of the myriad of behaviors that make me inwardly cringe.
It is not our place to be the manner police and as hard as it may be to watch a parent sit idly by and let their kids grow into the adults we all hate to interact with, it is just as rude (if not more) to insert authority where we have none.
Yet, I do agree that children should learn from those around them. Which is exactly why we, as responsible adults, neet to "lead by example." I even agree with the "it takes a village" sentiment, but as a parent, I get to decide who that village is. And it absolutely does not consist of strangers inserting themselves into our lives and telling my child what to do or not to do (with the exceptions I've mentioned).