Sorry to re-start the debate after a peaceful night's sleep, but... This idea that no-one is allowed to tell off/speak even-slightly-harshly to anyone else's children is interesting, innit?!
Quite a lot of mummies seem to believe no-one should speak crossly to their little angel - that is their job entirely. But then it follows logically that you have to keep constant vigilance, because every moment and movement of your DC's is your responsibility. You can't let DC develop independence in a natural, healthy way, because you have to stay with her/him all the time and be constantly alert for people s/he might hurt and/or annoy so that you can 'deal with' any problems before anyone else does. And how exhausting that must be! No wonder so many mummies drink so much wine!
Parents are not doing their DC any favours, if they try to protect them from any upset or tears. As they say in Yorkshire "We're not made of paper, we won't melt in the rain"... It's a crucial part of developing mental health to learn how to be upset and frightened (and other 'difficult emotions) and to deal with it and recover from it. It's called 'emotional resilience', and children who don't learn to cope with being upset by other people really struggle with school and friendships.
OP, from what you've said, I think you've given your DD several clear messages you probably didn't intend to give her:
- Her feelings are more important than anyone else's;
- Other people's behaviour/emotions can control her feelings (implication = she doesn't control her own behaviour/emotions);
- She can't cope with other people without your help;
- If/when other people are (even slightly) mean, she should be upset and disempowered; you and she can only function in the world if everyone is nice.
Whether or not the woman actually over-reacted, it was a perfect opportunity to help your DD learn to cope with difficult situations. Next time, perhaps, try a different approach: "Oops, you hurt that lady's toe, let's say sorry and see if we can help... Oh dear, she's still grumpy! Never mind, let's leave her in peace now, cos people sometimes need a bit of time to get over being hurt and upset, don't they"... And if you can manage it, I bet you'll soon watch your DD blossom into a more confident child, who no longer cries and clings to your legs in difficult situations :)