For me personally, the problem isn't so much the radiation exposure. I've been a radiation worker since the 1970's and understand the risk. But many do not understand it and then they (all of us) are presented with TSA and their management of the machines, which far too often comes across like a Three Stooges short. The TSA officers spout boilerplate phrases about the safety, and it is obvious they haven't got a clue about how the device operates nor do they possess any basic knowledge of radiation theory yet they act like they do. Hence the public fears.
While there may be no substantial increases in cancer as the result of the therapeutic or diagnostic use of radiation, there likely have been some cancers and deaths from it, although they cannot be conclusively attributed to it. It's one of those things where the public just has to trust that the government is being truthful, and that is a hard pill to swallow for many.