As I suspected, the story is a complete fabrication.
An EoZ reader contacted American Friends of Kaplan Medical Center and received this reply:
Your inquiry about the Kaplan Medical Center's refusal to treat a Palestinian girl because of a non-reimbursement of funds by the Palestinian Authority lacks not only facts but also is not based on the facts. Iran is not known to "love" Israel....Iranian media making up a story? Say it ain't so!
The Kaplan Medical Center's Children's Medical Center does not treat serious pediatric cancer cases. If the chemical or radiation treatment is not helping, the patient is referred and transferred to the Schneider Children's Hospital which specializes in these cases. This may have been the case with the sick girl in question.
If you would look at our website under: KMC IN THE NEWS you would find many cases where the KMC had saved lives of the children, regardless of their creed or provenance.
Here is one story about Kaplan treating a Gaza child who had been injured in an explosion that world media falsely blamed on Israel.