Different corporate processes work differently. I have seen some corporate performance review software where the employee is actually asked to review the written feedback (which should parellel the discussion) and to Agree or Disagree with it. Either way, the important part is that the employee does review it.
If that's not an option where you work, the next best would be something dated and in writing, so you can review it several times before you send it and be certain of the exact wording. Often email is a good conduit for this, as it gets logged and both yourself and the recepient can save a copy.
Truth is, the actual solution will take more than either one of these activities. It sounds like there's a really serious disconnect between what your management thinks is your responsibility and within your control and what you think. I suspect in the upcoming weeks and months, you'll need to have a lot of talks with your management and get clear about these things and make sure that you have the capability to take on the responsibility that they are trying to give you.
It's hard to say point blank "I won't take responsibility for that" as usually taking responsibility for work is part of the job and this will put you into direct conflict with your management where they can rightfully say "we told him to do this, and he refused". But saying "I can't fix X, Y, or Z, so how can I take responsibility for the overall outcome?" may yeild a better conversation. Best yet is to (in the future as you are doing work) be able to say "I'm taking responsibility for this, there's this problem (insert problem), and what I think is the best answer is this (insert answer) and to do that, I need to have this happen - can you help me get that done?" It's generally called "managing up" - it may be that there are cases where you can't take control, but you can still control the situation. That means you need to be open to your management saying "no, do it this way" but at least then you are having a productive conversation and taking responsibility, and if they give you direction, then you can't get in big trouble by following it.
You can also try taking your issue to HR or to upper management, but when it comes to day to day work and the evaluation of it, responsibility will eventually return to you and your direct management. You can log your disagreement with these outside groups, but it's honestly unlikely to change the situation.