Does this message about visa extensions in Thailand look legit?

Yes, people can get a document from their Embassy when you can not travel back to the country of origin or for some the country of the passport used to enter Thailand.

At the moment there are ways to travel back to your country, you have two options:

Go back to your country as long as this is possible on the normal way.

Wait till your last day of stay and hope somebody on the Embassy understand your sudden emergency and hands out the letter.