.. But it's also not murder, since they believed they were acting within their rights to make an arrest, and had no apparent intent to lynch or shoot the fellow,..
... they cannot claim the perfect right of self defense, but rather only an imperfect right, which subjects them to a charge of manslaughter.
It appears They have been charged with Felony murder, § 16-5-1 -
which does not support your imperfect self-defence /manslaughter claim.
