Only if you let them. The false positive thing is a nonissue that only arises from assuming you would respond to information a certain way.
I don't really get what this means. A false positive causes issues inherently - you don't know if it's right or wrong. It's noise which is bad for care, and it's anxiety-inducing for patients which is also bad. It produces worse outcomes for everyone. There isn't a "choice" or assumption here, you respond to a positive as if it's accurate until you know it isn't. This is a known issue. Hell Scrubs did an episode about the negative impact of full, generalized body scans on a patient's wellbeing decades ago.
That makes no sense at all, unless you're saying that people should respond to all such information by ignoring it.