However her relationship with David is not canon, the movies never implied one. Maybe its in the novels (shrugs). They did not even come across as friends, just colleagues on a mission. But it is a shame she was not a baddie in the movie, there are some good fanfics where she is just as guilty but due to Valaris loyalty to her she is never caught.
True, but still David pretty much sacrifice his life still...Not to mention the senselessness from his death probably made a convincing case that the Klingons are just not the kind of people to get a lasting peace with. David was basically a civilian and the Klingons involved just straight up killed him (I mean he resisted but he was unarmed and probably would do little anyway). Saavik is a Starfleet officer who just saw a Federation civilian die on her watch saving her.
While the relationship thing is iffy (heck, I agree with you on that now that I think about it), I still think that event could shook her up to not give the Klingons leeway about talking things out because she saw an attempt and it didn't work out.