OR perhaps this from the UNC website, which makes a bit more sense:

What is a Tar Heel?
The University not only uses the nickname "Tar Heels," but the entire state does as well. One version of the nickname's origin has the name first being applied to North Carolinians during the Civil War. One record talks of a battle in Virginia, where their supporting column retreated, but North Carolina troops fought alone. The victorious troops were asked in a condescending tone by some Virginians, who had retreated, "Any more tar down in the Old North State, boys?" The response came quickly: "No, not a bit; old Jeff's bought it all up." The Virginians asked: "Is that so? What is he going to do with it?" The reply: "He is going to put it on you'ns heels to make you stick better in the next fight."

Spaw