Correct. Treat parts of the face as individual focus points. If the interest is the lips then lips it is. If it's the balding head then go nuts with the hairline. If it's a plain portrait, the eyes would be the best and most effective focus point. No hard and fast rule. What's important is to effectively lead the viewers' attention where you want to. To me that is portraiture at it's best.
A lot of elements, but ultimately leads you to that one eye:
Photo by Caitlin Worthington