1. It's difficult to respond to whatever you were actually taught because you don't give us access to it. If you had a quote or a reference or something...

  I would be surprised if "Box-Cox is necessary" would have been presented as a general, unbending rule.

2. You present nothing of the criteria by which you judge the forecasts, but if, for example you use MSPE on the original scale (i.e. you transform back then measure performance using square error loss), then *even when the Box Cox leads to exactly the right model* you might still on that basis conclude it was worse.

3. Box Cox has parameters (at least 1, depending on what your model is and what you consider for transformation), so - as with adding parameters anywhere else - it may sometimes be advantageous and sometimes not.