1 rem of radiation exposure causes cancer with a probability of 0.05 % according to Wikipedia[1].
It seems such a scan causing a cancer would be due to a very low probability event on a cellular level. From that point of view the above calculation looks reasonable. It is only after that when the additional macroscopic influences caused by a specific person's body/environment come into play that your point applies.
This was interesting so I started from that 0.05 % per 1 rem and did the inverse calculation. For 2500 rem this gives about 1-(1-0.0005)^2500 = 71 % probability of developing cancer. I also made a plot from 0 up to 10000 REM[2]. The incident rate seems to be pretty much approaching 100 % around 10k, so our results differ by about a factor of 4.
25 at 100 rem, again 1 cancer, but they now have ARS (acute radiation sickness). This is interesting since one would think ARS would definitely cause cancer, but it’s only 1/25, whereas 1/3 of people will develop cancer.
8.3 people at 300 rem, which is the 50% threshold for death from ARS, but still 1 cancer.
I’d think 2500 CT scans/year is a typical number for a hospital. Can they be sued for causing that single incidence of cancer?
