One or more SEVERED FINGERS absolutely does justify an emergency response like calling for an ambulance. You know, "severed finger?" Meaning a finger that's been detached, ripped ragged, caught from it's bone and pulled off - that's what a severed finger is.
People in here are seriously arguing that it doesn't merit a call to an ambulance. As if a person in that situation is going to deduce the pros and cons of the situation at the time.
Common sense is too often a stranger here. Logic can take you far, but as in the case of this thread, much too far out.