Screening based on family history will miss the 75% of women who develop breast cancer each year who have no family history.   You are confusing results from the randomized, controlled trials where women who refused the invitation to be screened and died from breast cancer were still counted as being screened (non-compliance) and women in the unscreened control group whose lives were saved by screening are counted as unscreened controls (contamination).  Women who actually participate in screening have a 40% or higher reduction in mortality