The absolute decision to hire or fire is not required to meet the executive exemption under the FLSA but involvement in the process is required (for the executive exemption). The exact language is listed below.

"The employee must have the authority to hire or fire other employees, or the employee’s suggestions and recommendations as to the hiring, firing, advancement, promotion or any other change of status of other employees must be given particular weight."

Your involvement in the hiring process (the interview) would be evidence that your suggestion is given weight. If it is your recommendation to fire that is "pending review" by upper management you appear to be correctly classified as exempt. Involvement in both hiring and firing would bolster your employer's classification of you as exempt, but involvement in one process would be enough to meet this prong of the test.