Well, you have made my mind up. I think it is a reward for good behaviour.
I have only spoken to 1 other mum so can't give a wide view, but she said her daughter has worked out that if she takes the child to lunch she will get team points. The mum said her dd was quite cleaver in that way. My ds has not worked that out (probably not as quick), he was just thrilled to get team points for doing what came naturally to him.
I don't think it has been specifically said by the teacher "look after X and you will get team points." But the cleaver children can work it out for themselves. However, I take your point Twoifbysea, what happens when team points don't have the same attraction?
I believe the problem started when the child came to the school mid term. He was given a 'buddy', which is standard practise in the school, to help him settle. The buddy sits next to him, takes him to lunch and plays with him during breaks. Normally as the new child settles the child will meet other children and the circle widens.
Sadly because this particular child has Autism (Asbergers) he becomes very attached to whoever is spending time with him and very clingy. He doesn't like football and running around, he likes to sit and dig in the dirt and wants his friend to do it with him. Quite quickly parents were having 'quiet words' with the teacher to say please would you ask another child to be X's buddy because my child is getting fed up now.
The poor teacher knew that X needed to have someone be with him during the lunch hall and playground experience and would move on to the next child, until the inevitable happened and the parent would want a 'quiet word'...
Personally I think as X needs help to move through the processes at lunch, then a child should not be expected to do it. As for the playground, it is very sad.
To add, the child started 2 1/2 years ago but still is not able to go to lunch on his own and children still have to help him - which is probably why they give team points (albeit subtely) to children who will take him.