When a person is salary, they do not punch in, complete a timecard or get paid by the hour. They are not eligible for overtime,ever. If a person is hourly, they are paid overtime according the the FLSA. If for instance, she is paid overtime for any hours worked over 40, then yes, she can be asked to use personal or vacation time to make up hours when she is not actually working. Since the time off is due to slow periods, she can have a valid point if there is nothing stating such time must be used in her employee handbook. She would be within her right to ask for a written statement that showed the company policy which states that she must use that time.
If she is paid salary and never receives overtime, she can not be made to use her personal time. This would change her status to non-exempt and the company could then be liable for back payment of overtime.
If this doesn't help, please let me know.
Thanks,
Lisa