What about the dentist's uv gun?
(Unrelated to the first) Even if the probability is low, say 0.0001, of DNA damage happening after a single dentist visit, that still will result in hundreds or thousands of cases of DNA if the population is large enough, i.e. in every larger city.
Your dentist uses UV after every visit?
But those cells are grown from stem cells, and if they remain undamaged, their descendants (the brand-new epithelial cells making up skin) will begin their life already damaged.
With all that said, the underlying biology of cancer is extremely complicated and it's hard to evaluate the impact of things like this. Some amount of DNA damage happens constantly that bodies can clear up without any real long-term impact.
For a dentist visit, we assume that the increased benefits from infrequent x-rays exceed the low probability of cancer. I don't know about UV used in dental applications, though.