I've launched this defense before. You have to feel bad for Bill Clinton. Unquestionably, his presidency had the best record on civil rights and improving living standards for African-Americans of anyone since Lyndon Johnson. And here he stands as various Clinton surrogates have been (correctly) accused of trying to scare voters about Obama's past drug use, etc. Clinton makes a relatively innocuous observation, that Jesse Jackson won South Carolina twice with a coalition of heavy black support and modest white support, and the world explodes around him. Sometimes, you just mess up and underestimate how crazy people will get. This is particularly true because Clinton clearly has more respect for Jackson than the rest of the national media, so he doesn't think it's demeaning at all to be compared to him.
I say "partial defense" because Bill Clinton continues to just make shit up. After going on WHYY and saying "they played the race card on me", he later says "that's not what I said". Likewise he claimed, with no evidence that Jackson's white supporters were blue-collar, salt-of-the-earth types, while Obama had the backing of a bunch of effite college boys. I'll bet him dollars to donuts that exit polling would show that Jackson's white support in South Carolina was primarily from upper-middle class voters, as it was in New Hampshire.