The way I phrase it is "the fear of the thing is usually worse than the thing itself."

In his Personal Memoirs (https://en.wikipedia.org/wiki/Personal_Memoirs_of_Ulysses_S....), Ulysses S. Grant wrote of how he learned this lesson one of the first times he led troops into battle in the Civil War:

I received orders to move against Colonel Thomas Harris, who was said to be encamped at the little town of Florida[, Missouri], some twenty-five miles south of where we then were...

Harris had been encamped in a creek bottom for the sake of being near water. The hills on either side of the creek extend to a considerable height, possibly more than a hundred feet. As we approached the brow of the hill from which it was expected we could see Harris' camp,and possibly find his men ready formed to meet us, my heart kept getting higher and higher until it felt to me as though it was in my throat. I would have given anything then to have been back in Illinois, but I had not the moral courage to halt and consider what to do; I kept right on. When we reached a point from which the valley below was in full view I halted. The place where Harris had been encamped a few days before was still there and the marks of a recent encampment were plainly visible, but the troops were gone. My heart resumed its place. It occurred to me at once that Harris had been as much afraid of me as I had been of him. This was a view of the question I had never taken before; but it was one I never forgot afterwards.

It feels to me like he is just to taking the very old advice to "face your fears" and make it seem like he has something new to offer.

Yeah, but it goes a little deeper in the sense that sometimes you feel fear but don't understand it, and you can try to go deeper understandig and confronting the fear, or since you are not sure what is happening, let go the situation and try to hide, escape it, delegate it, distract yourself. The point is more about the sense of fear that you don't understand where it comes from, and you prefer not to dig deeper understanding the fear because you fear that you will find something ugly. And instead confront it.