Yes, an employer in North Carolina can fire an employee at any time for any reason. The legal question that really matters is: do you have a legal claim if your employer fires you because they made a mistake on your FMLA time? The answer to this question is dependent on several factors. If I understand your question correctly, your employer is counting an absence against you that should have been FMLA covered. If that is the case, you most likely will have a claim for violation of the FMLA if the employer fires you for an absence that otherwise should have been FMLA covered.