You failed to see the point. She is a cancer survivor because she has survived her breast cancer. But She is not 100% cured from her breast cancer.
For now - she is cancer-free. See the difference?
I repeat.... with emphasis - she is cancer-free
FOR NOW. There is always a chance of remission or spread. Meaning..... her breast cancer may have spread to other organ and it will take years for it to manifest.
That's the whole point of radiation and chemotherapy treatments - to reduce the chance of spread and perhaps to kill almost all cancer cells. It's the only best option we have now even though it's barbaric and primitive IMO. Dr. McCoy believes it so
Star Trek IV - The Voyage Home where the Enterprise crew traveled back in time in 20th century. Dr. McCoy was at the hospital and he came across this patient.
McCoy: What's the matter with you?
Patient: Kidney Dialysis
McCoy: *muttering* my god.... what is this, the dark age? *opened his doctor bag, gave her a pill*
anyway - she got a double mastectomy even though her right breast didn't have a cancer but she opted for it to vastly decrease the chance of cancer spreading.