When you fall 17 blocks down onto a vine, you still take fall damage. That is, you fall 16 blocks and the vine is the 17th block just above the ground. If you fall any other number of blocks onto the vine, you do not take fall damage. 

For context, I have a hole that is 17 blocks straight down that I would jump down, and I would use 1 vine at the very bottom to break my fall. I have tested it falling 16 blocks, 18 blocks, and other distances, and I would always take zero fall damage as the game mechanic intends. For some reason, it does not work for exactly 17 blocks.