What numbers are you using? Do you have a link?
According to this article,
N.C. crime rate sees sharpest drop in 25 years :: WRAL.com, NC crime rates actually fell sharply in 2009, and most major cities reported significantly lower rates. The three cities you mentioned had rate drops of 14% over the prior year.
Regardless, I think all three cities are very safe. There is crime, of course, but for the most part it seems confined to the sketchy areas of town. I would say most of the crime I hear about in the Triad is either domestic violence, drug-related, or larceny/break-ins. Fortunately we rarely hear about muggings or random assaults on innocent people, and I always feel quite safe in downtown Winston-Salem, Greensboro, or Asheville.