your questions regarding the game rules (improving the interpretation).

"if the presence of reinforcements can affect the outcome of the battle or the losses in the battle for either player.
The difference in losses was, if I remember correctly, as much as one imp!!!"

Did the losses have an impact? Yes, they did. The rules don't state how significant the difference in losses should be. It's not quite a case for a disqualification, but a replay could have been called. I don't want to engage in nitpicking, but such precedents encourage players to commit minor violations in the hope that they won't be noticed or ignored.