I have had thyroid surgery. My surgeon discussed the possibility of complications including trauma to the laryngeal nerves, which are very close to the thyroid and controls the voice box. Swelling or minor complications can cause loss of voice for weeks, sometimes (but rarely) it is permanent. I had a camera on a tube placed down my throat before and after my surgery to inspect the larynx/voice box to make sure it looked healthy before and after. The other possible complication was damage to the parathyroid glands, which are attached tot the posterior (back) of the thyroid in four places, two on each lobe. If the whole thyroid is removed, there is a higher risk of losing the parathyroid glands, which causes an inability to properly regulate calcium levels.
In my case, nothing was mentioned about losing the ability to control muscles around the mouth, and I have not previously heard of this as a possibility. I don't believe the nerves in the face are located anywhere near the thyroid, so my best guess is your friend is confusing the possibility of laryngeal nerve damage with loss of mouth muscle control.
The best way to minimize risks for thyroid surgery is to find a surgeon who performs many thyroid surgeries a year with a low complication rate. If your friend does need surgery, it is in his best interest to find out how many thyroid surgeries his surgeon performs a year and what his or her complication rate is. I was very lucky that my surgeon performs hundreds a year and her complication rate is lower than the national average.