There is some limited truth in what was said.
Branches are responsible for organising the work in the territory they cover. They will choose RC locations for example and manage the administrative aspects of the work without too much discussion with HQ. Of course there are top down processes and procedures. Larger construction projects are very much managed centrally. However on a day to day level the branch does not have to run every little detail past HQ.
When it comes to more serious issues like this then the branch has the right to change rules to suit local requirements. In the case of child abuse policies this will be limited to ensuring the process conforms to any legal requirements such as mandatory reporting. The hands of HQ in NY are tied in this case.
Does it ave the ability to change doctrinal situations such as two witnesses? Not unilaterally. If the Australian government made a law giving a victim the right to converse only with a woman for example, then the Branch would likely reformulate the policies to make some allowance for that. Any change would be agreed with HQ. It would be the minimum possible to meet the legal requirements.
No branch can make unilateral instructions about anything that has some interpreted scriptural mandate around it, like two witnesses or elders only being male etc. No branch would or could ever come up with changes to fundamentals like this. You would never see some schism opening up between countries where one country allowed female elders, two witnesses, gay marriage or whatever and other countries did not.
To illustrate the relationship with a slightly difference use case, cast your minds back to the Mexico v Malawi situation. If you consider the difference between how these were handled, it was not a branch decision as to how the rank and file were instructed. They did not say "this is what we will do in our country". The differences were from HQ. They decided that it was alright to treat the two situations differently. Neither branch had the power to say what they might have really wanted to do.
The same applies in these cases. Sure, the local branch might implement specific modifications to the core process but ONLY to suit the legal requirements of the state or country. They will never build heir own policy. It's not unknown for large numbers of, even whole, branch committees to be reassigned when they don't play ball with HQ.