I think it's a strong argument. It's not 'someone much later with fuzzy memories decided to interpret what they thought they heard', it's 'someone right there and then was so struck by what the revelation they just heard that they broadcast it to the world (and you can check that they did by looking at the Twitter timestamp)'.
Which do you trust more, a witness statement taken a minute after the crime, or made a year later?
That someone said something very revealing and immediately backtracked with an excuse "I didn't say what I said" is, on the other hand, deeply unconvincing.
How does that change the fact that saying "I tweeted it so it's true" is not a strong argument in a he-said-she-said debate?