I think the suggestion of reading a short statement recognizing the hardships suffered by those students who haven't been able to complete their graduation requirements due to forces beyond their control is a good one. Most likely, this girl is not the only one. Deaths in the immediate family, car accidents, and bad cases of mono can routinely cause kids to fall a class or two short of graduating with their cohort, and it's entirely reasonable to recognize these things.
At the same time, no, I wouldn't permit her to walk at graduation. I also frown on people walking at college graduation ceremonies when they haven't finished all their requirements yet. I feel graduation is a time to celebrate those individuals who have, well, graduated. She has not. Despite the one doctor stating that this is a form of punishment, she's not being punished by the school (though one could make a case that she's being punished by the cosmos). She's just not being celebrated for an achievement she has yet to make. There's a distinction there which I feel is important.