Hey Simon,
you got it pretty correct!
If the Walk Forward finishes with a better equity line this gives us the idea that the original strategy is not over-optimized.
And at the end, it does a complete backtest with the final parameters. If the complete backtest is a better strategy, we can use it. We have simply a better strategy and it is not over-optimized one. Because of the optimizer work just for the last segment, not for the whole period. The backtest is on the whole period.
After that walk forward optimization course from Petko, this thing got clearer for me :)