Actually, let me rephrase. It's a bad situation all-round. I assume you didn't tell your friend's kid to go in and argue with her teacher. (If you did, then you are a prick. Otherwise, I rescind the above.) At that age, kids want to tell people when they learn fun or exciting things (well, that's not really restricted to that age), but they don't always think through the effects of saying them. Now, I definitely do know a number of elementary teachers who aren't great at math, but even if the teacher is good at math, imagine their perspective. Off the top of my head, I can only think of a small number of options: 1. agree, move on, and have a bunch of kids who are either confused or are going around telling everyone they know "1 + 1 = 10" without understanding why; 2. scrap whatever lesson they were supposed to do and go into a long, unplanned explanation of how different number bases work and interact with place value; 3. tell the girl she's wrong. Quite frankly, none of these are good options.
I can't really fault you for teaching her fun math, but for an elementary teacher that's a really rough spot to be put in.
And yes, letting everyone be argumentative all the time is how classroom management goes out the window.