Sorry for the delay. Is there any reason you think they shouldn't? Sorry if I'm missing the point. Why shouldn't they confront a suspected shoplifter?
They are perfectly free to do that. Any person can be asked to leave their premises.
They are not in loco parentis and don't have to allow her to remain the store just because she is 10.
People who steal do sometimes conceal items in store before leaving with them.
They don't usually leave the store with them in plain sight.
I can't say why they confronted her of course. I suppose neither can you as she was not close to you. For some reason, she appeared to him to be suspicious. It is quite unlikely he picked on her for no reason at all. Life isn't like that. It might well have been an incorrect suspicion but that doesn't mean he wasn't lawfully free to confront her and ask her to leave. Stores can withdraw their invitation to any person at any time they like.
It wouldn't have mattered what age she was. Children are ultimately not their responsibility.
They are perfectly free to be overzealous if they want to. This is their property.
As you can ask people to leave your house without showing cause or reason.
That is a matter for you.
They are free to take a different view.
Ok. Good luck