Sorry, but still wrong.
I assume you also think that exposure to a single anthrax or smallpox spore will result in a case of the disease in the exposed individual? It does not, due to the same mechanism that protects individuals from cancer...the versatility of the human immune response.
Mutations happen constantly in body cells, but most never result in disease, as those cells are "culled" by the immune response. Disease only happens when the basic immune response is overwhelmed, either by an exposure to a high concentration of disease agent, or fast cellular growth.
Now, mechanisms that can stimulate the immune response (vaccination) and "train" the body to recognize and attack a disease agent, can actually prevent disease.
I do not, I did not say 1 cell remaining guarantees recurrence, I said anything less than 100% kill and you risk recurrence, and that is absolutely accurate.