In a recent game, I had a fleet of 4 ships. I then broke the fleet into 1 ship and 3...i sent the one to go kill a scout and then i was gonna send the remaining 3-ship fleet to an undefended starbase. I moved the one fighter, and the scout died. I then moved him again to use up his remaining move points. However, this time his old fleet of 3 fighters tried to move with him (even though it was clearly no longer attached to the fleet). I had to reload because I couldn't afford to leave that starbase undefended. After killing the scout, the individual ship and the fleet were no longer in the same space so I couldn't have selected both.

This has happened to me twice where I will disband a fleet, move a portion of it, and then the other portion will move on its own as if the fleet was still intact.