The Scotsman newspaper tries to make Lincoln's conscription intelligible to its audience and ends up labeling Andrew Carnegie a draft dodger.
I read this story and reverse the meaning. Carnegie did not use his acquaintance with McClellan, Thomas Scott, or other major figures in power to avoid the draft - if he had, he would not have had to hire a substitute.
At the point one needs to hire a sub, one has failed to dodge the draft.