She does not say this literally - the line about "war hero".
She is saying it because she thinks he deserves a medal for remaining gentlemanly as the Dems and Media wage war on him. She is only pointing out, otherwise, that he served honorably in the Texas Air Guard, yet these cretins even lied and slandered him about that. But she does not mean that he did heroic deeds in an actual war.
Unless, of course, you acknowledge that it takes guts and skill to fly an F-102, and we were in the Cold War.
As for his statement about "vigilantes", I saw when he said that. He was asked a question, before he or very many people knew what the Minutemen were about. Millions of Americans I am sure believed that these folks felt driven to take measures similar to law enforcement, because our own law enforcement was not working on the borders. The Media distorted what the Minutemen were about, and only after they operated for awhile did we see their tactics.
The only thing I fault him for is that after it became more apparent that they were not acting as vigilantes as he had feared, he would have done better to officially retract the answer that he had given to the reporter's question.
I think it is wrong to hold that against him as if he had never done anything else noble or good.
This is exactly why I find him unimpressive. A good and wise man who knew nothing of the Minutemen would have withheld his comments, but he didn't and he went ahead and incorrectly labeled them.