What wrong did the Union troops do? Guarantee the safety of the Freedmen?
A president being assassinated by an internal terrorist force would make the North angry. Hell, they were angry enough to pass three amendments giving rights to Black people even when the majority of them were extremely racist, the North isn't letting the South get away with murdering a President, especially a war hero. Many Radical Republicans would use this assassination to their political advantage, and many of those Radicals would think that passing amendments was not good enough, they would need to increase military presence in the South. After all, even with draft riots and weakening morale in 1863, the Union was able to mantain their current numbers. And don't get it wrong, all Republicans would frame this as a war on them, and having a powerful White man (instead of only black people and an extremely small number of poor whites) being murdered by the KKK would turn Northern moderates to the Republican side, even if they don't become Radicals.