I'm not sure why your cousin has been told that she's cancer-free. I assume she has been told that on completion of treatment there is no evidence of cancer.
Remission from cancer can be partial or complete.
Complete remission means there is no evidence of the disease following treatment.
Partial remission refers to the situation where the disease shrinks but does not disappear completely with the treatment.
I finished my treatment for breast cancer exactly 5 years ago, and am in complete remission. But no doctor has used the word 'cured', nor will they.
With some cancers, if after 5 years from diagnosis the the cancer has not returned, it isn't going to return, and so the patient can be considered 'cured'. Cervical and testicular cancer are examples.
For many other cancers, including breast cancer, while the chance of recurrence falls steadily, and is statistically greatly reduced after 5 years, it doesn't drop to zero.
Breast cancer can return at any time, even years after treatment, though the chances of recurrence drops with the passing years.
This doesn't mean breast cancer is never cured - far from it. The statistic that 75% of breast cancers caught early are cured is undoubtedly correct, but no doctor will ever assure a woman who has breast cancer that she is cured or 'all-clear'. I guess it can only be known for certain when they die from some other cause without ever having a recurrence of breast cancer. The fear is always there, though it takes more of a back seat as the years go by.
Rather than saying you're cured or cancer-free a doctor will say there is 'no evidence of disease' (or NED, my favourite word!); in other words, you are in remission