When "not only ...but..." coordinates noun phrases, inversion does not occur.
The sentences Ananja presents,
1) Not only the constant silence but also the refusal to even provide us some small measure of assistance in our quest for justice reflects the strong interests behind the fire.
2) Not only the CBI but all crime detection forces and prosecutors need to be independent of the administration.
...illustrate coordination of noun phrases: in Sentence 1 "Not only...but" coordinates the noun phrases "the constant silence" and "the refusal to even provide us some small measure of assistance..." In Sentence 2, it coordinates "the CBI" and "all crime detection forces."
"Not only...but..." coordinates more than one kind of sentence element.
Inversion can (but does not necessarily) occur when "not only...but" coordinates verb phrases,. For example,
Roger was not only living totally at her expense, but he later boasted that he had been supporting her lavishly
...may undergo inversion:
Not only was Roger living totally at her expense, but he later boastedthat he had been supporting her lavishly
More precisely, it coordinates main clauses, with the grammatical subject "Roger" being represented in the second clause by the pronoun "he."
When the coordination is between noun phrases, no inversion occurs.