I try to remember that my own kids periodically say rude things to others, and usually don't even realize they're being rude.
I'd like to say that I only intervene when necessary -- meaning, when the rudeness is affecting my child and she seems to need my help -- but a few weeks back, I was rather ashamed of a reaction I had to a child at our local homeschooling co-op when she informed dd2, when we were walking up the stairs from one class to the next, that it was okay with her to have one class with dd but she didn't like having to be with her for two classes.
I told dd, in front of the child, that this meant she (dd) could still go to the classes but she didn't need to sit next to this other child or play with her. The child was rather taken aback and said she was sorry, she didn't mean to hurt my feelings, but --
And I interrupted with something along the lines of "No, it's actually good that we know you feel this way, so dd won't be sitting next to you anymore." I put my arm around dd and we headed upstairs ahead of the little girl, who followed us up, and when dd and I started playing Candy Land because the teacher was running late, she asked if she could play too and I said okay.
And since I helped with the other class, I made it a point to be kind to this girl and make sure she felt included in all the activities, because, by the time the class started, I was feeling pretty much ashamed of myself for my immature reaction. Dd was never even that upset about it and, thankfully, it hasn't affected her interactions with the other child in the least.
So...ideally, I observe and see how my children are handling things and only intervene where necessary. But sometimes I act like a real jerk. Either way, we all learn something and life goes on.