When is it ok to correct a friend's child?

Today Keenan and I had a great play date with a very good friend of mine and her daughter. Her child is 8 and mine is 2 so you can imagine the advantages of having a big kid around at the park. I actually got to relax and have a normal adult conversation with my friend. Imagine that. She's a GREAT kid! I love her, she's very sweet with my son, and she has tons of spunk and energy that I enjoy and is one smart little cookie. Truthfully, she was the most excited human on the planet when I was pregnant....yes, way more excited than I was...and couldn't wait for Keenan's arrival. Her mom and I are also very good friends and have been for several years. We're the kind of friends that you don't bother cleaning your house for and that you can have a credit card declined at dinner in front of without embarrassment (and who'll also pay for dinner and not bat an eye). Dinner is exactly where I inadvertently corrected her daughter. We were talking and her daughter (who is 8 and can be that annoying silly and dramatic) started screeching like a bird and when we stopped to look at her she said "I have a question for you guys". She started to ask a question and I said "But we were talking and that was rude." She of course sulked for a bit and came around and all is well. I'm pretty sure that my friend didn't really care because I think what popped out of my mouth was exactly what she was going to say. But my question is this:

When is it ok to correct other people's children?

My opinions on the subject are that 1) if my kid is doing something naughty and I'm catching it, please give them a correction, 2) if I catch your kid doing something naughty, I'm going to give them a correction. I can see arguments for and against both of these opinions. I know that not all parents have the same parenting styles or same issues they feel like they want to address. What I might find needs to be corrected might be something another parent can overlook. This can be awkward. Methods of correction can vary. I tend to say what I don't like about the behavior and ask that they refrain from doing it with a please usually inserted in the sentence and I try to keep my voice neutral. (Not so with my child when he's pushing it, the stern voice comes out). For most children I find that having an adult other than their own parent correct them tends to make a bit more of an impact. They become shy or embarrassed. And there's that old saying that it takes a village to raise your child and I know darn well in my neighborhood growing up that if I was caught doing something I shouldn't not only was I told to knock it off but my parents knew about if before I ever got home. But there are freaky parents out there that go ballistic when other people correct their children and then it just becomes horribly awkward. Also, I don't even like it when my Keenan's dad corrects him too harshly so if someone else is correcting my child I would hope for some restraint.

The other questions I have on the subject are how much should you push it? If you've asked for a behavior to be stopped and a child doesn't comply how far do you push it? Do you correct children other than yours in front of their parents or wait for their parents to step in? How far do you let it go when a parent isn't addressing a behavior before you step in? I don't know that I would be so quick to correct because their own parent should be doing it and I'm pretty sure that unless it's a major safety issue that if a child doesn't respond to a first comment on their behavior that I probably am not going to push it too much but maybe try to restructure the situation. Lastly, how close do you have to be to this child and/or the other parents, before you feel comfortable disciplining them?

I would just hope that Keenan grows up knowing that he better mind his p's and q's around any and all adults and sassiness and defiance are definitely not acceptable behaviors whether I'm around or not.

Opinions?