Ok. Looking back at the course of this conversation, it has taken some twists along the course. There are a few issues which should not be confused, but dealt with on an individual basis. Perhaps they can also be sub-categorized as follows:
1. Allowing kids to begin talking to strangers
a. By simply greeting
b. By a formal conversation (asking directions etc.)
This category was NOT the initial attention of the OP.
2. Allowing kids to reply to strangers
a. Reply by greeting to a greeting
b. Going into a formal conversation that the stranger begins
This category was also NOT the initial attention of the OP.
3. Strangers replying to a conversation that a kid started on his own
a. Reply by greeting to a greeting
b. Going into a formal conversation that the child begins
This category was the initial attention of the OP.
Somehow the whole thing was intertwined one into another.