If it's something that happens 9 times a day every single day of the child's life, then maybe. But generally speaking, no. I personally will not tell my child to "Shut up!" because it's rude and unnecessary and I don't remember my parents ever saying anything like that to me. "Nobody asked you" is not in and of itself a cruel thing to day and is an example of a phrase I feel can be said without rudeness.
Further, public humiliation, as long as it is not done on a daily or otherwise routine basis, is not abuse. It is an effective way of teaching a child that there are consequences for their actions and that often those consequences are immediate. The police certainly aren't going to care how humiliated someone is while they are arresting them, so why should parents feel guilty or bad about calling attention to inappropriate behavior while they are out in public with their children? It often doesn't do any good to bring attention to behaviors hours after the fact (such as your example of complaints about the child's behavior at home), but to do something embarrassing in front of your kids in public in response to a behavior that is happening at the time can be an effective way of driving home the point that their behavior is unacceptable and will not be tolerated. and for kids in the "too cool" stage of development, public humiliation can be a great reminder that if they don't want the world to know about something, maybe they should just not do it in the first place.