A normal person cannot bite their own finger in half because the body has things in place to prevent you from overly injuring yourself like that. You would stop yourself short and just cause pain, maybe bleeding, but no long term damage.
Now someone else’s finger is a different story. Also people with certain medical disorders can ignore the feelings stopping them from biting their own finger off.
Would’ve been better if they said he had to get a rabies vaccine.
The chances of getting rabies is extremely small, but the second you say that will result in them immediately vaccinating you for the sake of safety as that window can close fairly quickly. And if you change your story they typically don’t care because people scared of vaccines change their story all the time.