Sadly, as usual, the media gets it wrong. They always do. Here's a link to the original article: Journal of the AMA.
Notice that there are other details, just in the summary alone, that the press isn't covering. See my two posts above for more information, too: It's been known for many years that lumpectomy with radiation has the same results as mastectomy IF the patient is eligible for a lumpectomy. Not all patients are. Yet, because the media only gives readers half the story, many people believe every woman is eligible for the less intrusive surgery.
I don’t think the study takes into account any genetic testing or factors, and those would weight the decision one way or the other. But what the summary does imply is that they are comparing apples to apples. They found extra cancer in 1-3% of the amputated breasts. That is probably what one would expect to find in a ramdom sample of amputated breasts. The study shows that amputation has no effect in most cases (probably all except the ones with genetic predisposition).