In the Cochrane review using only the best randomized trials, among women who had undergone screening, death from breast cancer went down, although the 95% confidence interval for the effect includes relative risk (RR) = 1.0 which simply means the finding is not statistically significant, that it is possible there is no difference in breast cancer mortality between the two groups (RR = 0.90, 95% CI 0.79 to 1.02).
But here's the rub. Even as screening apparently reduces the risk of dying from breast cancer, the all-cause mortality (death from all causes) was the same for those who didn't undergo screening and those who did. In other words women's chances of dying is the same whether they get screened or not. Needless to say no woman in her right mind would gleefully queue up for screening knowing that her chances of dying from breast cancer would be reduced only to have her chances of dying from something else increased (including death from the consequences of radiotherapy and surgery to treat breast cancer).