I think I might rather say impassioned rather than fierce, but that aside, I think you have a good point there.
In coming up with the word "fierce", I was trying to find the word to best describe a mother defending her cub. To say the mother was "impassioned" would be far too mild, but to describe her as "vicious" would suggest that defense of her cub was secondary to her interest in attacking other animals.
If someone uses a shovel in self-defense because it happens to be the only weapon handy, striking one's attacker until they are clearly not a threat would be fierce. Continuing to beat them into a bloody pulp even after they are quite conspiciously dead would be vicious. Fierceness is good, but viciousness is not; coroner's-inquest problems notwithstanding, someone who continues beating an attacker who's already dead may fail to notice the other attacker sneaking up from behind.