Now, through various dialogue options you can get Graham to tell you that Caesar refused to acknowledge that Graham didn't die when lit on fire and tossed into the canyon. He want's to appear powerful and unstoppable, and admitting that he failed is not something he is willing to do. Even losing the Dam the first time he managed to move the blame from himself and put it onto Graham, saying that his Legate failed him, not that he failed. He uses frumentari and assassin's to try and finish what he failed to do in the first place, with no success. I imagine that, even if his assassins had succeeded, they would likely be put to death before his Legion found out what they were being commended for in order to hide that he failed from them. If you kill Graham and Daniel and take the map instead of completing the quests, the White Legs are still denied entrance into the Legion. It comes back to him being unwilling to admit defeat, having white legs in the legion telling the soldiers that they earned their place by killing Graham would be akin to them telling the soldiers "Your master failed, but WE didn't".
I can't imagine any good way to write a path that the Courier could take to assist them. Graham tells you up front that Caesar won't admit defeat, and even if you didn't take the dialogue options to hear this, you could reason that the Courier understands that Caesar would be displeased with having someone telling others he succeeded where Caesar failed just by the fact that he put blame on his Legate instead of taking responsibility himself. It would be poor writing for the Courier to do it anyway, with full knowledge that he would be defeating his own purpose, that of assisting the Legion, by doing so. The only way I could imagine this to work is if you were to start Honest Hearts straight away after leaving Doc Mitchells home, having no knowledge that NCR and Legion were in the mojave, and even then I don't think you could write a compelling story with that.