Trump’s problems are self-inflicted by wording his tweet so stupidly. If he started with “In my opinion,…” then he could have said anything and Twitter would have no basis for any message.
As written, he is presenting the text as fact from The President of the United States and the force behind the office. Twitter was absolutely correct to add something, anything, to indicate that the statement was not a proven fact.
Now, in my opinion, he is using the power of the Office of the President for personal gain with his Executive Order. That is headed down the path of Watergate and he needs to be careful. I would not be surprised if that Executive Order is headed to the Supreme Court or the House.