That seems like it would be the most important part of the whole article, and it was left out.

It’s possible that the standards of evidence in a civil case is low enough that they don’t have to demonstrate a causal link. Only that there is radiation in the air and that radiation causes cancer.

The article acknowledged that you cannot say for certain what caused her cancer. The court determined, however, that the increased radiation exposure qualified as a workplace hazard that increased her risk of cancer and was therefore a contributing factor. At least, that's the way I understood it.