Unfortunately I'm not sure how a judge would ever justify that. Half of a book is still under copyright of the whole thing. Original music in the background of a movie is still copyrighted as part of the movie, even if a loud action scene is taking place on top of it. So even with a dial tone sound overlaid, that wouldn't change the fact that the music part of the recording has been published.
:(
https://www.copyright.gov/circs/circ14.pdf
EX: https://en.wikipedia.org/wiki/Pride_and_Prejudice_and_Zombie..., https://en.wikipedia.org/wiki/Aladdin_(1992_Disney_film)
I don’t know if publishing 1/2 a book would protect the first half or not, but presumably the second half would have entered the public domain in your hypothetical example.
But what was described isn't "half of a recording". Imagine the "publish to extend copyright" applied to books too - would publishing the book with half the text blacked out still extend the original book's copyright?
That's just my naive take on it (i know nothing about copyright law). Your movie music argument might already be enough to show that I'm incorrect.
Subtract the dial tone and the music part is "half" the total copyrighted work (which includes the dial tone).
But the music part is still 100% copyrighted. Same way that if you publish a book with 200 pages, pages 1-100 are still 100% copyrighted even though they make up only half of it.