Question about Parallelism! from 5th ed SC Manhattan

[make_wishes_2010s]

On page 62, the question asked me to correct the underlined part of the following sentence:

Dr. Crock's claims have been not corroborated by other scientists or published in a prestigious journal but have nonetheless garnered a great deal of attention from the public.

And the answer on page 64 is:

Dr. Crock's claims have not been corroborated by other scientists or published in a prestigious journal but have nonetheless garnered a great deal of attention from the public.

My question is (and I've looked through many posts about this sentence but none of them answered MY confusion):

I assume the question is testing us about the "not... but..." parallelism. Since the first"have" in the sentence appeared in front of the "not", why do we still need a "have" after "but"? I know that in "parallelism" sentences we should repeat "subordinators" in order to remove ambiguity, but "have" is not a "subordinator"; it's just part of a "working verb". Why can't the following sentence be correct:

Dr. Crock's claims have not been corroborated by other scientists or published in a prestigious journal but nonetheless garnered a great deal of attention from the public.

Thank you very much! :)

[RonPurewal]

The discussion of "subordinators" and "working verbs" is miles over my head, so I won't go there. In fact, the problem is that you're thinking about those things, rather than about the meaning of the sentence.

These are two different parallel constructions:
"X ... but Y"
"not X ... but Y"

"X ... but Y" is used for ideas that contrast with each other.
If there's a "not" in this type of construction, then it isn't a connector (i.e., it's not paired with "but"). It's just part of one of the two contrasting ideas.
Laura did not study for the test, but got a perfect score on it.
("not" is part of the pink thing)

"not X ... but Y" is used for ideas that reinforce each other.
Ron not only designed the dress, but sewed it himself.

Here, you're looking at a contrast. So, it's just "X, but Y". It's like the sentence about Laura, above.