That's actually nonsense. You most certainly can cut off someone's finger and use it to unlock their phone. I'm not aware of any capillary scanners on phones...
TL;DR: Cheap phones use optical sensors (can be fooled by an inkjet). Older high end phones and some new ones use capacitive scanners which require the actual finger plus an equivalent capacitance which can be faked by holding the finger with your bare hands (making sure to get close to the actual finger tip). Might take a few tries but it'll work. The latest tech uses ultrasonic sensors which measure the ridges of the fingerprint incredibly accurately. Enough so that blood loss may result in failure but I doubt that any phone's sensor is going to require that level of accuracy (do you press your finger with that precise amount of pressure every time?).
