I both agree and disagree.

I agree that by adjusting the phase, you are shifting the wave forms position (but not its form), but for the same reason as described above, I believe it is shifted not to place a null from the sub
alone, but rather not to detrimentally combine with
other sounds at the listening position.
In principle, I agree, but the rolloff of the crossover from speakers to sub is not a brick wall filter. Therefore in practice, there will be some small duplication of sound occuring.
This is reaching the limit of my present understanding of such matters. If anyone else would like to chip-in, or correct me if I am mistaken, please feel free.
Regards