Ling Ling told me that in China begging is illegal. The government does take care of people, even if they are disabled. She said in many cases, there is a "handler" for the beggars, and they take the money that is collected.
When I told her about the woman standing so close to us, and even getting in between us, she told me that many times these beggars are pick pockets. That's why they stand so close.
I will still take these situations on a case by case basis, but her words did give me food for thought. And now I'm glad that I made the woman leave. I think my instincts were right, but my conscious self was just worried about doing the polite thing.