I'll try and put out the argument here- First, I must say that I am a white american, and have no first hand experince in dealing with the racial issues some minorities say they experience. So all I can do is relay what has been explained to me as best I can.
I had a long talk with another military officer I served with a number of years back on this subject.
He came from an urban area, and had some good insight. One of the reasons he said was that many African-Americans don't actually have ID. The old, the young, those who don't drive, etc. While much of America has a driver's license and is depenant on the car, much (well, a significant number, anyway) of the minority community is not. It's viewed by some of them as one more way "the man" can try to take away the right to vote. Another thing is (he explained to me) that while it is common for whites to move and change their voting address when re-registering a car, or changing an address on a driver's license, in his community is was not so common. Sometimes people moved to live where they had to live, and didn't change an addess with anyone official. Again, part of it is no license offices in the community- and no car. So it is difficult to change your address several times between elections. He said within his community, it was common practice that "you came from someplace, so even if you move around, you always come back to vote there". People may move many times, but election time was the one time when they came back to the neighborhood where they voted, and cast their vote. However, if there are poll challengers, and the poll challenger asks you to prove you live where your voter ID says you do, well, that can lead to someone not being able to vote.
I don't know the factual basis for this, I only can relate what I have learned from asking about this issue. It certainly gave me interesting perspective on the lives of those less fortunate in our society. If I had not asked, I would have simply assumed that there was an effort to rig the voting. I now know the issue is FAR more complicated than that, and for knowing that, I feel I have learned a lot.