The issue at hand wasn't whether he ever misrepresented himself like that, but whether he did so in the context of this particular event - i.e. when he was being interviewed. I'm not aware of any video evidence of that, nor did any outlets referenced the video you linked to as their basis for the claims that he's a Vietnam vet. The reason why they did so is because he told them that he is a "Vietnam era vet", which is misleading (as Snopes rightly points out), but not outright false.