There are a handful of findings on an emergency X-ray that stop a room. A crescent of gas beneath the right diaphragm is one of them. It usually means a hole has opened somewhere in the digestive tract, allowing air to spill into the abdominal cavity, and it usually means the patient is going to the operating room.
Most of the time, reading is correct. A perforated hollow organ is by far the most common cause of free air in the abdomen, and the finding is treated as a perforation until proven otherwise.