You ask - isn't moderation the problem they're trying to solve. This gets to the heart of the matter. What is the actual problem Facebook are facing here?
I read the WSJ article and the quotes from the internal documents. To me the articles and documents are discussing this problem: their content moderation is very unreliable (10% error rate according to Zuck) therefore they have created a massive whitelist of famous people who would otherwise get random takedowns which would expose the arbitrary and flaky nature of the system. By their own telling this is unfair, unequal, runs counter to the site's founding principles and has led to bad things like lying to their own oversight board.
It's clear from this thread that some HN posters are reading it and seeing a different problem: content moderation isn't aggressive enough and stupid decisions, like labelling a discussion of paint as racist, should just apply to everyone without exception.
I think the actual problem is better interpreted the first way. Facebook created XCheck because their content moderation is horrifically unreliable. This is not inherent to the nature of automated decision making, as Gmail spam filtering shows - it works fine, is uncontroversial and makes users happy regardless of their politics. Rather, it's inherent to the extremely vague "rules" they're trying to enforce, which aren't really rules at all but rather an attempt to guess what might inflame political activists of various kinds, mostly on the left. But most people aren't activists. If they just rolled back their content policies to what they were seven or eight years ago, the NYT set would go berserk, but most other people wouldn't care much or would actively approve. After all, they didn't care before and Facebook's own documents show that their own userbase is making a sport out of mocking their terrible moderation.
Finally, you edited your comment to add a personal attack claiming I'm making "off topic political comments". There could be nothing more on-topic, as you must know from reading the article. The XCheck system exists to stop celebrities and politicians from being randomly whacked by an out of control auto-moderator system. A major source of controversy inside Facebook was when it was realized that the system was protecting political incumbents simply because they were more famous than their political challengers, thus giving the ruling parties a literal exemption from the rules that applied to other politicians. The political nature of the system and impact of moderation on politics is an overriding theme of concern throughout the documents. You can read the article for free if you sign in - that's how I did it.