This is partially correct, partially wrong.

As many have commented, flipping a signal by 180° cancels it out. However, this is only true for static noise though. Transient noise cannot be canceled out completely, because you would need to see into the future to know which signals to play to cancel out the noise.

The ANC headphones I own mainly cancel noise through passive shielding of the ears. The “active” noise canceling feature is not contributing a lot.