There are many types of treatments for cancer. The patient is told about them, the doctor gives his professional advice and the patient is left to make the decision of what type they'll seek, if any. Their choice.
In this case the family has been consulted on the various methods of treating this particular cancer and they, as a family have made their choice.
I do not believe for one second that the mother and father of this child are not taking into account EVERY detail of EVERYTHING they've been told. I do not for a second believe they love their child any less then I love my child. They are seeking treatments.
They've been told about secondary cancers that are caused by Chemotherapy. So she may well survive the cancer she has now if given chemo therapy, but since she is susceptible to cancer maybe she and her parents feel it's not worth having her survive this cancer only to spend many years waiting / expecting a secondary cancer. That's a life sentence of a different sort. And she can die from the secondary cancers. A horribly painful death while her parents sit by feeling intense amounts of guilt for having forced her through the first round of treatment.
Treatments linked to the development of second cancers
Chemotherapy
The cancer most often linked to chemotherapy (chemo) as the cause is acute myelogenous leukemia (AML). In many cases, myelodysplastic syndrome (MDS), a bone marrow problem that is sometimes called a type of cancer, occurs first, then turns into AML. Acute lymphocytic leukemia (ALL) has also been linked to chemo. Chemo is known to be a higher risk factor than radiation therapy in causing leukemia.
Some solid tumor cancers have also been linked to chemo treatment for certain cancers, such as testicular cancer.
Alkylating agents
Certain types of chemo drugs called alkylating agents have been shown to increase the risk of AML when used to treat certain cancers like Hodgkin disease, non-Hodgkin lymphoma (NHL), ovarian, lung, and breast cancer.
Alkylating agents known to cause leukemia include:
Mechlorethamine
Chlorambucil
Cyclophosphamide (Cytoxan®)
Melphalan
Semustine
Lomustine (CCNU)
Carmustine (BCNU)
Prednimustine
Busulfan
Dihydroxybusulfan
The risk gets higher with higher drug doses, longer treatment time, and higher dose-intensity (meaning that more drug is given over a short period of time). Studies have shown that leukemia risk begins to rise about 2 years after treatment with alkylating agents, becomes highest after 5 to 10 years, and then declines. Alkylating agents often cause MDS first, which then progresses into an acute leukemia.
MDS and leukemia that develop after treatment with alkylating agents can be hard to treat and tend to have a poor outcome.