It seems likely that what he gave her was a more general treatment for organ failure. Perhaps medical science had made some progress in kickstarting the body's general healing abilities using stem cell therapy. If you could induce the production of certain stem cells, it's possible that the damaged tissues could be repaired.
We only have a small glimpse of what happened, but it's possible that further examination would reveal that her other organs may have all repaired themselves to some degree. You could also reason that the delivery system was optimized in a way that would concentrate the effect on severely damaged tissue.
One thing we can't be sure of is the extent of the repair. He gave her a single dose. That may have been enough to repair the damage enough to restore kidney function, but we don't know how much or how long the effect would last before degeneration started again.
Another factor to consider is the speed with which the therapy worked. You'd still be constrained the normal metabolic process, as well as the conservation of mass and energy. However, we have to allow for some hand waving due to the time constraints of the movie. :)