The tenet that radiation cannot spread a fungus is incorrect. Fungi radiotrophic effects in the literature is exactly aligned with radiation making cancer worse. See cryptococcus neoformans and ionizing radiation triggering a melanin synthesis virulence loop. See the lichen that grew on the international space station. Other fungi including sacchyromyces are also included here. You can match this phenomenon to reports of mammogram induced cancers of which there are studies available.
You are correct, the fungus theory is testable.
I replied to J Bostock. To address the “wouldn’t it be infectious”, that mental model has the assumption of being able to actually detect transmission. That type of thinking seems inherited from acute infectious models rather than chronic disease modelling. In the chronic pathogenic model, progression of disease can be slower and causal attribution can be unassigned. To understand this point, see link below re: latency in cryptococcus neoformans, where the fungi can go dormant in white blood cells for years or decades.
https://pmc.ncbi.nlm.nih.gov/articles/PMC7324190/
For what it’s worth I found OP extremely valuable.