Presumably, the website has a history or reputation (such as Stripe or Plaid’s official website). I guess Twitter might serve the same function, especially since this is a real person posting under their supposedly verified account, but I do not use Twitter, so for me, it is less easy to verify the source.
A better example is the tech emails twitter account that posts screenshots. How would I know if they are fake or not?
I would think a website with links to the source material such as the court filings showing the emails on a government website would be preferable.