Feigning ignorance due to intimidation is not better than simple ignorance. Doctor are morally responsible for doing no harm. I do recognize such is not always easy, for reasons you have mentioned.

My 40something wife would love it if our HMO would stop calling and emailing her 6 times a year to get a mammogram. She has explained clearly to her gynecologist her reasoning, that she is absolutely not going to get a mammogram before age 50, but the annoying calls do not stop. (We shut off our ringer, and use a Google voice number for people we want to her from.)

Much as I sympathize, breast cancer survivor groups have many characteristics of a religious cult. They have paid a high emotional and physical price for entry, and as a result they are so bought in to the idea that the treatment-torture saved their lives that they have only a limited ability to think rationally about health issues anymore.