"...this is the first war America has been in where the number of casualties is small enough that it would even be theoretically possible for a Defense secretary to sign each condolence letter personally. "
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Technically, she is correct. The Secretary of Defense position wasn't created until after WWII (not sure of exact date at this very moment and I don't have time to google).
BTW...Don should have signed the letters personally. But he doesn't deserve the media attacks and he should be spending his time trying to win the war and bring our troops home as victors.