What I find fascinating about this episode, is that it illustrates how cultural misunderstanding is a huge driver for continued tensions between the Empire and Federation.
The Federation and humans especially try to be pacifists and explorers and are ashamed of their ability to be fearsome warriors. Ashamed of the barbarity they are capable of. The Klingons misunderstand this, and think the federation are either weak or duplicitous. That the federation is pretending to be peace loving so they can stab the Empire in the back, or wants to avoid war because it is weak.
Meanwhile, humans think diplomacy is always the answer. When dealing with Klingons, being honest about humanity and the federation's capacity towards violence would go a long way to easing tensions. If the doctor was known as the butcher of J'Gal, this would have helped the federation seem more like a worthy opponent and therefore potential ally. Instead he allows a Klingon to take the credit, and the federation ends up being represented by the worst kind of Klingon, a coward who ran from battle. What the doctor did was arguably very honourable in Klingon eyes. He killed a coward, who killed children, but ran when faced with a real warrior.
It's also politically relevant today, where pacifism is seen as a weakness, while others underestimate how strength and the threat of violence often prevents wars or the fact that sometimes extreme violence ends wars and potentially prevents further suffering.