I know I may be overreacting, but when the dentists try to convince me that the annual x-ray of my family members is the same as being outside in the sun for a whole day, I try to explain it with a similar analogy; getting exposed to small amounts of x-ray over a long period is not the same as getting exposed to all of it in a fraction of a second.
They insist it because it is covered by insurance, and that I shouldn't worry about the cost. I have to clarify that the monetary cost is not my primary concern.
I have now learnt to simply say No, and agree to sign a waiver that's required by the insurance company.
I am okay with getting the x-ray if a professional has a legitimate reason to suspect there's something hidden that can be better investigated by getting an x-ray. My family has received x-ray, MRI, CT scans, ultrasound, etc. but only when its benefits outweigh the risks; e.g. bone fracture, pregnancy, concussion, etc.
As I said, I may be overreacting, but I'd like to err on the side of caution when it comes to my kids' and family's long-term health.
edit: s/by I'd like/but I'd like/