caesar wants graham dead. i think it's safe to say the whole incident in zion is the plan to eliminate graham without letting the legion as a whole know graham is still alive. certainly other high ranking legion officers know the truth (someone has to explain why all the frumentarii aren't coming back and explain why so many are being dispatched to zion).
ulysses did not confront graham. i forget if he explains this. in fact, i pretty much forget everything ulysses said about graham. but ulysses' orders were definitely to organize the white legs to wipe out graham and his tribe.
for all intents and purposes, graham is dead to the legion. he's never going back, he does not seek revenge, he just wants to be left alone. it is caesar who needs graham dead. his ego can't handle it if graham is alive. also, caesar has no intention of assimilating the white legs into the legion. they are a tool, and when they're purpose is served, they will be thrown away.
if your character is into protecting the innocent, certainly the sorrows and dead horses are innocent? as innocent as you can get in a post apoc wasteland anyway. perhaps your character could come to an epiphany about caesar's bloodlust and spare graham?
i think what would be ideal for your character would be to eliminate the white legs, save the sorrows and dead horses, and kill graham. but that's not possible, unfortunately. unless you can kill graham while on the final mission? i've never tried.
very good question here, i'm not really sure how you should play this out. depending how free thinking your courier is, it would be equally plausible to wipe out graham and co. as it would be to help them evacuate.
end note: my one major criticism with HH is you can't join the white legs. otherwise i think it is a very good dlc. emphasis on dlc.