I may need to rethink this

I have developed a strategy for dealing with the embarrassing things my kid blurts out in public.

You know the kind of things I mean. You're passsing a stranger with an oddity of some type, and your child's eyes lock onto the person and he makes an observation at top volume.

"Mommy, that lady is FAT!"

"What is that thing on that man's FACE?!"

"Ew! That boy STINKS! What's WRONG with him?!"

Et cetera.

In the past I had always had what I'd call the usual response: the Shush-and-Rush.

That is, trying to silence the child, hurrying away from the scene, and hoping the person hadn't heard.

I have learned that this does not work. The person heard, all right. Everyone in the whole store heard! And if they didn't, they sure heard it when the child repeated himself as you were dragging him away. "But why is she so FAT, Mommy? WHY?!"

So what I've started doing is addressing the remark directly, in full view of the offended party and the rest of the world.

Example: I say brightly, "Well, sweetie. Some people are fat and some people are thin. Everyone is different; that's how God made us, and it's okay."

The major advantage to the Direct-Address is that it makes the child stop repeating the inappropriate thing, because he feels listened to. And that's all he wants, is an answer to his question. Really. He's not trying to be irritating. (Usually.)

The other thing that I hope this strategy does is show the remarked-upon person that I care about their feelings and am not just allowing my child to say hurtful things with impunity. This part, unfortunately, does not always work out the way I plan.

Enter the One-Armed-Kid.

We were at the McDonald's playground and a little boy came in who had the lower half of his arm missing. Little Girl was FASCINATED.

She came running to me. "Mommy! That boy has ONE ARM! He only has ONE ARM! What happened to his ARM?!"

I put on my calm-friendly-and-bright voice. "Well, sweetie, sometimes people have one arm. Everyone is different; that's how God made us, and it's okay."

She persisted. "But Mommy! What happened to his ARM?!"

"I don't know," I said, nonplussed that she hadn't stopped yelling yet. My strategy was failing. I tried to remain matter-of-fact and said, "Maybe you could ask him."

This was a BIG mistake. She ran directly to the boy.

"WHAT HAPPENED TO YOUR ARM?!" she yelled in his face.

The boy screamed and ran away from her. (Do you blame him?) She came back to me and I told her that maybe he didn't want to talk about it. Finally she went back to play without asking more questions.

A few minutes later I saw the kid's mom grimly putting on his shoes and dragging him out of the area. He was crying. I felt horrible. Had my child and I driven him away from the playland? Obviously we'd offended the mom with our agressive directness.

Still, I'm not sure how I should have handled it. 

Does anyone else have a better idea?