The difference is that a screenshot may be fake. If the intermediary is revealing user private messages, it’s a stronger evidence than just making up a photoshopped screenshot.
For example rooting a phone by hand is pretty hard. Many tools exist to do it automatically.
That assumes that the decrypted messages aren't signed (e.g. via HMAC), no?
But there are plenty of other ways to implement this. Digital signatures. Or if facebook stores the ciphertext, the recipient could simply reveal the decryption key for the message. Or facebook could compute a MAC over the ciphertext with a key neither participant knows, then the recipient could reveal the ciphertext and decryption key, and facebook could verify the outer MAC to verify authenticity.