I think this article is alarmist and fake news. They're not fun, they're not 100% accurate, but they are important and do identify life threatening tumors.
@Sanguine I agree. It is not fun for the beasts to be mashed in the machine for a number of seconds/a minute, but it is over fast.
One time, I was referred to a surgeon due to a tiny spot in one breast. He told me he was sure it was nothing, but if we didn't get that out and check it, and it was cancer, then we would be sorry we didn't do it.
So, I went in for the surgery. I was put on a gurney and rolled to the x-ray department. This guy did nothing to deaden the area, put me under a machine, located the spot and stuck a needle into the breast to where the spot was. Can you say pain? Then they rolled me out and the motion of the gurney made the needle keep moving and it was major painful. Got to the room and the anesthetist saw how much pain I was in and said, "I will give you something to stop the pain." He knocked me out and I woke up after it was over.
The tissue was sent for analysis and it was not cancer. I didn't have to worry that cancer might be growing in that breast.