They acknowledge that, per their own measurements, only one part in 200,000,000 of the energy is nuclear. The rest is from "some competing process".
The competing process must also be nuclear. There is no chemical fuel, and no chemical changes are observed. They did not know what this other process could be, but later research indicated it is probably some form of D+D => helium-4.
You may not agree with the authors that this competing process must be nuclear, but I am 100% sure that is what the authors meant. I know this because I spent a lot of time with them and discussed this in detail.