The suggestion inferred from the "forced up the rate of mutation" statement, is that the genetic code was responding to the presence of the disease by mutating. This is not how it works. Mutations exist and may give selective advantage to those who contain those traits. When such an advantage exists, over time, the inheritors of the favored trait will tend to be more successful in reproducing. Short of increasing radiation near the gonads (as suggested in post 17), mutations--either to their nature or rate--occur randomly.
I agree with you regarding the resistance surviving and reproducing itself. Is this trait a mutation? Is the lack of resistance a mutation? Is a genetic weakness in the immune system a mutation, or vis-a-versa?
We each have the genetics to reproduce with various traits. We may have the genetics to reproduce either with this plague resistance or without it. That does not mean that my DNA is undergoing change in this process.