Since that topic was raised some events have brought the question to national prominence. And the way polls read, a lot of Americans seem to think it doesn't matter. Competence is everything.
Personal integrity is expendable.
Now, I don't want to dwell on this particular example, but rather want to look at much larger, more serious historical examples of exercising leadership without exercising character. Rather than examining the current microcosm, look at the macrocosm to draw the issue more starkly. It may not matter to the leader in question. Character, integrity, high personal moral standards, conscience, are not essential to success. A person can lack all these things and still be very successful.