Not everything that makes a good headline is true.
There are many things said for and against mammography that you may find in the news. Here is a list of websites that help explain the pros and cons of screening. In summary, the main risk is that the more mammographies you have to track changes in the breast, the more likely there will be something that needs followed-up. The risk in this situation is that being asked to do a follow-up test may cause stress, additional cost and/or unnecessary biopsies. However, if what is found turns out to be cancer and it is caught early, then the result could be life-saving.
Visit the American Cancer Society page that explains mammography in further detail, along with a more detailed explanation of the pros and cons of screening.
Breastcancer.org also has an explanation of mammography risks and benefits in several articles found here.