you've said it yourself. "she is very private with this" if you want her to use the quilt, which why make one if not to be used, then stay away from anything that would indicate it for/because of the cancer. I would recommend getting a nice soft flannel without the pink ribbons and telling her it to because of this.
Quilt will be used, she won't mind showing it to others. And she will know the cause of it being made and given.
When my sister beat her leukemia she got rid of all her pink ribbon stuff. So done with that and don't want it to ever come back.