I'm not sure that's true. Anyone can claim to be "rrmm" but only one person has that set of fingerprints.
The bigger issue I see is that 'rrmm' is an identity I assumed. I have many different identities. I only have one set of finger prints. (Fingerprinting to unlock a local store of keys would fix some of this problem, but I am fond of plausible deniablity in identification).
If a biometric sensor can be tricked by a body part that is no longer attached to the body, that's a serious issue. But AFAIK at least modern sensors try to verify if it's still alive and then there's also the biological effect that a body part quickly changes its properties if it is no longer supported by the body.
The biggest danger in that is probably criminals who don't know that it is likely that a detached body parts stops functioning.