It's not "certain" that Obama won Charleston. I'd know, I live in West Virginia.
Romney won the county by less than 12%. The city has only 50,000 peeps but the county has almost 200,000.
By comparison, Romney managed to win my home county (Campbell KY) by 20%, but Obama won the largest central city (Newport) pretty handily. The city has 20,000 while the county has 90,000. By that standard, Obama probably won Charleston by about 8%.
Obama won Charleston, WV in 2008 with 58.2% of the vote versus McCain's 41.0%. Even if the city swung to Romney by as much as Kanawha County did, that would still leave Obama winning Charleston by something like 52/47. I find it hard to believe that the city of Charleston swung to Romney more than the overall county.