Yes, you made a point without name calling. The picture painted was still the same, but, no reference to the word brat was contained in your post. That seems really, really significant to you, so, I want to make sure I state that clearly.

It really ties right in to my point about addressing someone by the title, and how it doesn't really convey anything different to me. It is just a word, the respect is behind the action, not the term. Just like your description of the child's behavior was left without a 'label', but, the meaning (brat) was still inferred.