I'd much rather have a 90% detection rate without an X-ray than 100% with. Destists are very trigger-happy with X-rays, in part because of the extra billing, but mostly because it makes their job easier and prevents mistakes.
The estimates of the hidden costs of radiation risk are tentative at best. Some people have inherently higher risk and many are not aware of it. Either way, it can take years or decades before the effect plays out. By then, no one is going to implicate the original providers who pushed for an elective X-ray.
Also, note that not all ionizing radiation is alike. The exact spectra are different and the exposure intervals are very different, so the comparisons to environmental sources don't necessarily hold.