I have actually witnessed this phenomenon myself. When my dad broke his hip he called out to me and when I came into the bathroom he was propping himself up on the sink. He had broken his hip and actually caught himself BEFORE he fell.
Your dad was fortunate, in that he caught himself.
I know a 96 yr. old lady that had a hip replacement last January. She's doing superb! Within a few days after surgery, she was up and walking. She rarely uses so much as a cane these days.