Twitter is merely labelling a tweet as being factually incorrect, it's not hiding the content.
The difference would be one is a company, the other a real person. No need for the company to get involved.
People who ignore the correctios and other tweets will ignore the company anyway.
Surely you understand that the company posting a fact checker is a more credible source, and that there are plenty of twitter users who, even if they disagree with Trump, may not be aware of the facts.
Would you trust Elon Musk to put truth under tweets from his company? With his behaviour in the last month(s) I wouldn't trust him with shit.
The next step is Google putting "fact checks" beside search results? Or what? Or a ministry of truth?
Im from Germany, and we see what's going on in America. And we all saw it happening already here, years back.
But I guess every nation needs to go its path and needs to fix their problems on their own.