I think this case brings up a very good argument on the statutes. I don't have the Tennessee self-defense law, but let's look at Texas
Texas PC § 9.31. SELF-DEFENSE wrote:
(a) Except as provided in
Subsection (b), a person is justified in using force against
another when and to the degree he reasonably believes the force is
immediately necessary to protect himself against the other's use or
attempted use of unlawful force.
(b) The use of force against another is not justified:
(1) in response to verbal provocation alone;
(2) to resist an arrest or search that the actor knows
is being made by a peace officer, or by a person acting in a peace
officer's presence and at his direction, even though the arrest or
search is unlawful, unless the resistance is justified under
Subsection (c);
(3) if the actor consented to the exact force used or
attempted by the other;
(4) if the actor provoked the other's use or attempted
use of unlawful force, unless:
(A) the actor abandons the encounter, or clearly
communicates to the other his intent to do so reasonably believing
he cannot safely abandon the encounter; and
(B) the other nevertheless continues or attempts
to use unlawful force against the actor; or (5) if the actor sought an explanation from or
discussion with the other person concerning the actor's differences
with the other person while the actor was:
(A) carrying a weapon in violation of Section
46.02; or
(B) possessing or transporting a weapon in
violation of Section 46.05.
(c) The use of force to resist an arrest or search is
justified:
(1) if, before the actor offers any resistance, the
peace officer (or person acting at his direction) uses or attempts
to use greater force than necessary to make the arrest or search;
and
(2) when and to the degree the actor reasonably
believes the force is immediately necessary to protect himself
against the peace officer's (or other person's) use or attempted use
of greater force than necessary.
(d) The use of deadly force is not justified under this
subchapter except as provided in Sections 9.32, 9.33, and 9.34.
Looking at the highlighted sections above, there was never really anything more than verbal provocation going on (b)(1).
Additionally, look at (4)(A); the wife was mouthing to the guy and arguing back and forth (provocation). Next the husband goes an retrieves his pistol from the car and comes back. They never tried to deescalate the situation or back away from it. Had they walked over to get in the car in an attempt to leave, and the guy followed them and prevented them from leaving, then he got his pistol, he might have had better justification.
In the end, I think the alcohol involved and the bravado of both of men and the woman lead to a very stupid decision that ended up costing one man his life and another probably most of the rest of his life in jail.