Who reads a diagnostic fetal ultrasound? I thought the doctor would be in the room during it.

MD reads - may scan. The physician (maternal-fetal medicine specialist or radiologist) will read all the studies that the sonographers capture and may scan personally as needed.
Doctor. Reads study. Won't be in the study unless technologist needs help.
A doctor. A doctor will read your ultrasound, but they may look at the images later to make their report. In some practices the doctor will come into the room (or even do the exam themselves), but in others, an ultrasonographer will take all of the pictures and the doctor will review them later and send a report to your obstetrician or midwife.