As a mother that has been through this exact thing, and fallen for it ONCE, I would tell you they are full of C*rap. I have had two big babies, the first by c-section without labor after being scared into it by tales of baby too big to be born and shoulder dystocia. I so regret it now. My daughter weighed 11 pounds 5 ounces and had a 16 inch head (of course, she never went through labor) and at the time I thought I had made the best decision. But I so regret missing out on her first day of life because I was in pain or a narcotic pain relief fog. I couldnt' keep my eyes open to hold her, look at her, or nurse her. I'll never get those moments back.
I figured it out by my next birth, and had a homebirth and my son weighed 12 pounds 1.6 ounces and also had a 16 inch head. Was my cesarean necessary? Clearly now.
This is something that OBs use all the time. THey fear a big baby. The best thing to do is stay unmedicated and refuse an induction or a c-section. A study last year came out that had the data that inductions for big babies had not bearing at all, no advantage for babies or mothers, they just caused more cesareans.
Get on the ICAN (international cesarean awareness list) if you want more info about cesareans and why this is just a bogus reason. Your body will grow a baby that will fit through you. Concentrate on gestating and getting your baby in the best position for labor. Anyway, the ICAN list, go to ican-online.org for info on that. You would hear from sooooo many women told this exact thing, and then we go on to birth even bigger babies the next time. By the way, I am only 5 foot 3.
If you are interested in my birth story, do an archive search for "pablo felix" and you should find it.
Good luck, please dont' make the same mistake I did and have an unnecessary cesarean.