According to the National Radiological Protection Board (have a look @ https://www.hpa.org.uk/web/HPAwebFile/HPAweb_C/1194947310610), "For the vast majority of dental projections the pelvic area is not irradiated and an acceptable course of action would be to explain to the pregnant patient that a dental radiograph delivers such a small dose to the fetus that the associated risk can be regarded as negligible".
You are not a patient, I know, but according to the same document, as long as you are at least 1.5 metres away from the X-Ray beam, you are safe.
The same document says that lead aprons should be used by staff, taking care of storage (hanged and not folded to avoid ruptures of the lead coat).
It seems your boss is right: you are safe if you wear protection and keep 1.5 mtr away from the chair whilst taking the X-Ray.