It does sound like someone has been saying this to her in the playground! Good for her that she is standing up for herself, hopefully she did that in the playground too. I have done the same as Marydean and explained it about health and wellbeing more than the fat vs skinny issue. I have always emphasised the everyone has feelings, hopes and dreams no matter what shape, size they are and they should all be able to try to achieve those dreams if they choose to do so! It's important that she knows that its not okay for someone to be calling anyone names, esp. fat! If this is happening it needs to be reported to the school, you have no idea how many young children end up with eating disorders from a young age because of these sort of taunts!
I hope that you can get some answers from her and that she can be comfortable in knowing that she is beautiful inside and out!