> Does it not work to say
No. It does not.
A diagnosis of "you might have cancer but the probability is low and we should just watch it" is not something that most people can psychologically take.
For more than half of the population, that kind of understanding is simply untenable.
And, even for people I knew who could understand it, several of them had so much anxiety that it drove their blood pressure up and it was better to just go get the biopsy so they didn't wind up with a stroke or heart attack.
In addition, "mortality probabilities" are a lot harder to psychologically absorb when you are 50 than when you are 20.
By the time you are 50, you've probably had more than a few of your friends and family in a coffin from a "low probability event".
Emotions are difficult. At some point, I will get diagnosed with a positive prostate screen (practically all men who live long enough do) that will almost certainly be "We should keep an eye on it." I hope I can weather it with the aplomb of my engineering background. We shall see.