This is simply not true. A calorie is a calorie might be true, and its hard to know which is healthier for any single fresh vs storage example but plenty of chemical processes are going on. It could certainly be the case that a small number of storage examples where particular changes occur cause particular risks that account for a significant portion of cancer.
Respectfully, that's a crock of nonsense.
"It's not at absolute zero, therefore there's some chemical process going on, therefore we don't know if it's causing significant portions of cancer"?
The number of things you can say that about is frankly infinite. You have zero reason to believe that any of the "chemical processes" that happen to an apple (or any food) in long term storage have anything to do with cancer.
This is a great example of correlation not equaling causation. You might as well say that writing years starting with a "2" could cause particular risks that account for a significant portion of cancer because of the different motions of our hand affecting our lymphatic system etc etc.
Irresponsible fearmongering with no foundation whatsoever.