> But we seem to understand the processes by which cell mutations, and subsequently cancer, and produced.
We certainly seem to understand many of the processes by which cell mutations are produced, but that's not the same as all of them, and, perhaps more importantly, what we do understand about how cancer is produced is that there are lots of factors besides cell mutation involved, and those of them that we do understand in general terms aren't understood in detail, and aren't sufficient to explain the entire process.
> But the probability of this study having failed to control for some other variable is higher than the probability of an as of yet unknown process allowing microwaves to produce changes in the chemical bonds holding together DNA.
That seems more like a statement of subjective plausibility than a supportable statement of quantitative probability, and, moreover, in order to be relevant to the result seems also to falsely assume that it is necessary to "produce changes in the chemical bonds holding together DNA" to alter the incidence of cancer. We already know that even when a potentially-cancer-inducing genetic mutation exists, various other non-genetic factors in the body (including qualities of the extracellular matrix around the cells which have the mutation) play significant roles in whether cancer actually develops. Its quite possible that if there is a cellphone-to-cancer link, that the mechanism doesn't involve changes in the frequency of genetic mutation at all, but affects on the body that affect the whether cancer manifests when a potentially-cancer-inducing mutation has arisen through other means.