It's an interesting, although perhaps controversial point of view. Hare (apparently) was a Reservist who completed his enlistment and was honorably discharged. But, he may never have served the requisite 180 days of continual active duty time. As such, he's probably not eligible for Veteran's benefits, although I'd have to check to see when the effective date of that particular statute is.
In any event, does that mean he can't call himself a veteran. I'm not sure.
I don't have all the facts, here ...
but in My Own Personal Definition of "Veteran", an honorable discharge is definitive. If you have one, you are one.