Integrity versus Honor

I just saw a video which told a story about Abraham Lincoln. The story was that Lincoln and his good friend were walking in the forest one day and his friend asked Lincoln to a bottle of whiskey to which Lincoln declined. Then his friend asked Lincoln to a cigar to which he refused but this time he told why. He said to his good friend that when he was small he sat by his mother on her deathbed and it was her final will that Lincoln would not ever smoke or drink to which he has kept up all these years. Alright, now I actually have a problem with this story. The whole point of me watching this story was to learn about integrity, but is that really what Lincoln is portraying? Lincoln did not smoke or drink because of a promise he made that he ensures he will keep, but not because he knew those things were wrong. Of course Lincoln knew those things were wrong but would he have still kept up this abstinence if he never made a promise with his dear mother? That story was not a matter of integrity but a matter of honor. Of course I am not denying Lincoln’s purity, but I am simply saying that this was not an example of integrity. Integrity should be of your own free will, not because you kept an important promise.