What can we do about systemic lies regarding Monica's suspension?
She's not suspended. She was de-modded. Which I'm going to use to make a point instead of correcting it with an edit: We need to be careful what we say about this situation, the words we use, and the things we focus future discussion/debate/support efforts on.
I think Tim's answer on the question you're talking about sums it up pretty nicely: We don't discuss these things publicly. Many ships have sailed, including the one where SE kept their own advice and wouldn't have supplied comments to the press under this age old adage. But here we are.
There's a big part of this that's gone public, and that part consists of conflicting reports of the events (what SE so far has said publicly is contradicted by Monica). But we need to remember that even more may still be private, and falling under SE's policy of not discussing suspensions/demoddings publicly.
What can be done to prevent this and get the facts out there for debate?
What we can to to stop lies and misinformation from spreading further is to keep in mind the facts (that X was said by Monica or SE about the situation), and avoid putting our own interpretations of what was said over these, turning cold hard facts into subjective interpretations. We need to keep in mind that there's two conflicting reports out there already, and when talking about these things we should be careful to make sure our readers know both.
I feel bad about 'get the facts out there for debate'. Too much of this has already gone public and done (irreparable?) damage, and I hate to think what might happen in the future when we make 'getting the facts out there' the new standard in these situations. We're probably best off making do with the facts that are out there now, and respecting that parts are going to be kept private from now on. It's not ideal, it outright sucks (even for me, I'd love to know more too)... but it can at least give me some hope and a sense of security that if anything ever happens to me or others, we won't end up mangled by the MSE rumor mill.