Mine are 13 and 6 and I'd say, having had one very easy child and one more "lively" and "challenging" one, and now that they are a bit older, that I actually feel even more strongly about this.
My DD is the sort who, had it gone unchecked, would have been clambering over seats and disturbing other people but she isn't. She was never allowed to, and she was never too young to learn.
She would rather run everywhere than walk so she must hold my hand when we walk through a busy restaurant/pub and I explain that she might run into someone, someone might trip over her with a hot drink etc. And, as hard as she finds it, she really, really tries and (for the most part) succeeds.
And when she doesn't, I apologise sincerely. There is no way I would ever, or would have ever, just turned a blind eye to her behaviour and left her to it.
Like I said earlier, they both get compliments on their behaviour but if anyone thinks it was a fluke and I'm a smuggy smugster patting myself on the back for my fantastic parenting when I was just lucky, they couldn't be further from the truth!!