In this case, they sent a "press statement" response instead of a "FOIA response". The FOIA response would have been just the "there are no written records" part plus the boilerplate.
They realized that this is a press story about to blow up, and that if they don't make a statement the press will just write "USSTRATCOM TWEET RAISES HACKING FEARS. WERE WE ONE KEYSTROKE AWAY FROM GLOBAL THERMONUCLEAR WAR?" with a "We contacted USSTRATCOM but did not receive a response [in the 3 minutes between asking and posting]" so they made a statement.
They realized that this is a press story about to blow up, and that if they don't make a statement the press will just write "USSTRATCOM TWEET RAISES HACKING FEARS. WERE WE ONE KEYSTROKE AWAY FROM GLOBAL THERMONUCLEAR WAR?" with a "We contacted USSTRATCOM but did not receive a response [in the 3 minutes between asking and posting]" so they made a statement.