Sentence Correction

Computerization and modern methods of managing voter registration have improved the integrity of election results while at the same time they have placed unprecedented trust in a few private corporations, having been ignored by the mainstream press since their nearly silent rise to power more than a decade ago.

(A) while at the same time they have placed unprecedented trust in a few private corporations, having
(B) while at the same time placing unprecedented trust in a few private corporations that have
(C) while they have placed unprecedented trust in a few private corporations at the same time, and have
(D) but placing unprecedented trust in a few private corporations at the same time that have
(E) but at the same time place unprecedented trust in a few private corporations, having

Please explain the answer

OA B

What is the source of the question? Honestly in parallelism vs referrent to corporations force me between A and B. But placing as an participle may be compared to have improved in early part of the sentence so B is ok.

Issues: while introduce simultaneous actions since the two things here, integrity of results and trust in private corporations are simultaneous the two structure joined with while is better. The contrast shown in D and E is so wrong. So the only option left to explain is A and C, and have ... in C is wrong there are only two items to be mentioned here as explained earlier and that second item is done through while, so and have is incorrect. The Verb+ing in A refers to whole preceding clause and not only to corporations the intended meaning. So A is incorrect.

The question is from the website www.gmathacks.com