Reproducible certainly, – predetermined decidedly not: unless the original was a cast iron cert from beginning to end.
Most battles are going to have 5(?) outcomes – strategic victory, tactical victory/winning draw, draw, tactical defeat/losing draw, strategic defeat.
If games replaying historical battles flip flop from strategic victory to strategic defeat too often there may a rules error, but it may be a finely poised battle to start with or there may be player error, or any combination thereof.
A cast iron cert that consistently produces opposite results to real life probably suggests a rules error, but there may be hindsight problems. Some battles that produced significant strategic victories seldom follow the same result in tabletop refights because of this whatever the rules used – Waterloo anyone? (not a cast iron cert by any means I know). And Austerlitz usually requires draconian set up and or house rules to get the same flow of battle as the original.
I totally agree that ‘I prefer what I believe to be an “accurate model” that allows me to make different choices than the historical counterparts and see what happens’. If those different choices make no difference to the outcomes at all I would suggest that either that modelling is faulty or the rules writer has a very deterministic view of the world.
Rules written specifically to give an adventure film style game (we aren’t going to kill the hero off in the first reel/combat are we?!) will not of course be bound by the above considerations.