“Veteran status” is, according to multiple online government sources (Hint: Search “Determining veteran status”), reserved for a person who served in the active military, naval, or air service, and who was discharged or released therefrom under conditions other than dishonorable. Reservists do not necessarily.
As a 28 year veteran, I consider a reservist or guardsman who satisfactorily completed their service to be a veteran.
Unless he tries to get a VA loan or care at a VA hospital, you need to find a real issue with this guy. There appear to be plenty.
Reservists who have served honorably on active duty establish veteran status and may therefore be eligible for VA benefits, depending on the length of active military service and other eligibility factors. In addition, reservists who are never called to active duty may qualify for some VA benefits.