Baby too big for natural birth?

I am in Sth america and my wife is 41 weeks and 5 days pregnant. The doctor at the private clinic first wanted to induce at right on 40 weeks without giving a good reason. she went back today at 41wk 5 days and the doctor told her to get a scan, the doctor who did the scan said the baby is too big for my wife to give birth naturally, and she would have to get a caesarian. Otherwise it would be too risky and they wouldnt do it. She hasnt had the opportunity to speak to her original doctor yet.
According to the scan the baby is 3800 grams (8.37 pounds) hardly big! the circumference of the head is 34.3cm (14.7 inches) also I believe actually under the average. The placenta size, amniotic fluid, heartbeat is all normal. The baby is in the right position and my wife is fine. She is not a small girl either so it seems to me the doctor is full of (/&% and either just wants to able do a quick, time managed procedure, and possibly at the same time make more money as the caesarian costs more. This is our first baby, given the stats is the baby really too big??