All-over itching with no rash can be a sign of Intrahepatic Cholestasis of Pregnancy, which is a serious liver condition that is dangerous not for mama but for baby. Your friend's doc is right that there is a high risk of stillbirth in the last few weeks of pregnancy if the condition is untreated. It's rare, but it is serious, and I think it is one of the few warranted reasons to give induction serious consideration.
The best source of information I know of on the subject is http://www.itchymoms.com/
I had cholestasis with my twins, and we wound up delivering early after I did a bunch of research, and I'm happy with the decision. We also wound up going with a variety of treatments during the last few weeks including Urso to help flush the excess bile acid.
The condition goes away within a few days or weeks of delivery.
If there is a rash, especially on the trunk, you'd suspect PUPPS like the PPs said.