However, I fear you may have also oversimplified some issues. If you were to show this episode to older women they would probably take it as entertainment value only due to a number of factors, namely 1) they are women at the age where breast cancer is a real threat, and 2) adam conover is a young male comedian with no background on women's health or medicine in general.
However, the one point you made about talking about this subject assuming your patient is afraid of a mammogram. This is assuming that your patients know what a mammogram is and what it's looking for. Yes, the lay person will know that it's to look for cancer. But that is it, nothing else. Adam presented his show from the stance of the outsider with no knowledge of how medical practices are. You said it yourself that performing biopsies are a means to determine what type of cancers there are, and this may not be exactly known to patients commonly.
As a personal opinion I think the conversation shouldn't be to fear monger, but more to ask engaging questions and for doctors to give detailed explanations about what it is they are doing and why.