Government-selected "trusted flaggers":
Nonetheless, under the DSA, the status of trusted flagger is awarded by the "Digital Services Coordinator," which is a national authority responsible for supervising the services of online platforms. The DSA allows law enforcement agencies or profit-seeking industry organizations to apply for the status of a trusted flagger, the notices of which must be treated with priority. - https://www.eff.org/deeplinks/2022/02/enforcement-overreach-...
Oh, and executive-branch agencies can order take-downs, without a court signing off:
Article 8 empowers national judicial or administrative authorities to issue mandatory takedown orders directly to “intermediary services" such as social media networks. In its recent vote, the Parliament rejected EFF’s suggestion and the proposal by the Civil Liberties Committee to limit these powers to independent courts. Instead, the Parliament followed the Commission’s proposal and allowed a broad category of non-independent authorities to exercise this power.
Brussels in a nutshell...
Finding of fact is a function government carries out thousands of times a day.
A court (deciding who commited murder, etc) is not a government.
As for advertisments, we decide for ourselves.
It's hard to imagine this isn't what ultimately happens. It seems to be a tall order for an EU court to compel speech from an American company in a political sense. In this case, Google can and I believe will stop offering youtube in the EU until the EU says that Google's proposed "fact-checking" system is Good Enough.
(Not to mention how gross it feels to insist that someone has not stated the correct facts and must do so or face a penalty.)