I believe your information is out of date.
In November 1996, the citizens of North Carolina voted to amend the State Constitution to allow for a gubernatorial veto (Section 22 of Article II of the North Carolina Constitution). All Public Bills other than bills making appointments, proposing constitutional amendments, or revising districts are presented to the Governor on the day following ratification for the Governor's approval or veto.
Yep. I had lived in NC pre-1996, when the Governator indeed lacked the veto. But that's not really a valid excuse for my mistake. Mea culpa!