Not "dishonorable." It's "Other than Honorable." Big difference. Not that it should matter, but that may be one of their talking points if this pans out.
Couldn't they just report that Kerry did NOT receive an honorable disharge?
Yes. Huge difference. (1) A DD can only be granted after a criminal conviction (i.e., General Court-Martial); (2) a discharge under other than honorable conditions (a.k.a. UOTHC, UO, or OTH) is granted in an administrative discharge proceeding; and (3) even in the wake of a conviction by court-martial, an officer cannot get a DD, only a "dismissal."
If in fact this turns out to be true (and I will believe it when I see it), we need to make sure we have our facts straight. Let sloppiness be the hallmark of CBS, not Freep.