Is it actually true that cancer will ever be cured fully?

Yes, it depends: Cancer is not one but many different diseases. Some cancers are curable, notably leukemias in children, hodgkin lymphoma, neuroblastoma, and many early stage cancers, e.g., breast, colon and prostate cancers. Improvements in medical care are improving survival for many cancers.

Not any time soon: We are treating cancer much more successfully today than in the past. However, most advanced cancers have the genome destabilized, and evolve resistance to treatment. I do not expect that such cancers, once they have spread and are no longer operable for cure, will be curable even 100 years from now.