It happens more than you might think.

If it’s a request without privilege risk, workloads aren’t crazy and the requestor writes them well, same day service happens.

Writing these things is like a grant, there’s an art.

Legally they have to reply in 20 days, though that's not exactly well enforced. One day is still quick, they were likely looking for a good outlet to announce what happened.

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.