The all-other-causes death rate for the refusers in the treatment group was 38 per 1.,000 women, versus 21 for those who chose to get the exam. It is true that screening was *associated* with this difference, because the two groups did differ in whether or not they got screened, but it doesn't make sense that screening *caused* the difference, since the death rates in question were from everything but breast cancer. To find the cause we have to identify some other way in which the two groups of women differed, and that's not hard - one group selected themselves for screening, the other group selected themselves not to be screened. Because of this opportunity for self-selection, this part of the experiment - comparing the examined and refused women - was an observational study (even though the treatment versus control comparison was a controlled experiment), and we need to worry about PCFs. The main one in any observational study of health is health status at baseline - it is likely that the women who went out of their way to get mammograms were more concerned about their health, and therefore in better health to begin with.
Remark: There may also have been an effect due to the experimenters not being blinded in this study, as follows. It was pretty easy for the experimenters to tell who was in the treatment group versus the control group, and also who was in the examined versus the refused group, so if the experimenters had wanted to they could have given better care to people in one of the three groups than in the other two, biasing the results. There is some evidence that this occurred in another part of the experiment: why was the breast cancer death rate for the refused group (1.5/1,000) lower than that for the control group (2.0/1,000)? Neither of them got screening, and we have already seen that the baseline health of the refused group was unusually low;why is it that they ended up with a *lower* breast cancer rate than the control women? Well, maybe the experimenters paid particular attention to the refused group because they knew they were part of the treatment group, and they wanted the treatment to be successful. If this kind of bias could occur in one part of the experiment it could occur in another part