You are correct.
On the subject of a tactical win or even a strategic win during this period there are examples that contradict the status quo.
One that comes to mind is at the Battle of Port Republic, Stonewall Jackson put to flight one Union Army to his front while another (Fremont's) appeared on the battlefield to his rear. Jackson's goal had been to evade a trap and fight his way out of it, he (actually Ewell) had already beaten Fremont the day before at the Battle of Crosskeys (leaving the field to Fremont). After dispatching the army to his front he did not turn to fight Fremont on the same battlefield, he instead turned to his right and left the area. Now Fremont, frustrated that he did not appear quick enough, unlimbered his artillery and shelled the battlefield that was occupied by hospitals, ambulances and many wounded of both sides, killing many. Why? The speculation was he wanted to claim to be last on the battlefield, therefore claiming the right to victory.
But of course Jackson is historically the undisputed victory (correctly called decisive victories) of both of these engagements because he accomplished what he wanted to do.