So, we know that the SOP for a carrier is to get its planes off the deck and to a nearby air station when it comes into port. So why would an A-4 launch when the carrier is docked?
I would guess your dad saw a plane that was scratched from flight operations on the day of the flyoff - possibly a missing or damaged part. Once they get into port, they could get it repaired, but then it’s still sitting there on the deck or in the hangar, possibly interfering with what they were trying to do with the carrier, or else not participating in training with the rest of the squadron.
Since the A-4 is a very light aircraft, and that delta wing gives a lot of lift, it might well be that the best way to get the plane off the deck and back to the rest of the carrier’s air complement was to fly it there, probably with no payload, a really low fuel status, and the lightest pilot in the squadron at the controls. I’d guess an A-6 or F-4 might have presented more of a challenge to get off the deck.
So while I’m not sure it should be quite considered “flight operations,” it is an interesting historical curiousity.