Unlike water, sweet berries, and cobwebs, twisting vines don't protect the player under certain circumstances. To reproduce, set RandomTickSpeed to 0, then place down a twisting vine. When falling from a height of 12 blocks, the vine won't protect from fall damage. When falling from a height of 13 blocks, the vine will protect from fall damage.
This also applies to weeping vines, normal vines, scaffolding (when sneaking), and ladders (when not hitting the top). It seems to apply to all blocks with the #climbable
tag.
It seems there's another case where they don't protect: if you have 0 horizontal movement.