We know for several reasons, both practical and empirical. First, Variety posted a report on the pic which pointed out that Bieber had filmed something for Funny or Die on the same day, which Bieber confirmed in a tweet. In the wake of the Batfleck mania, this is exactly the kind of prank the humor site would use to mock the fan outrage at the Affleck casting.
That aside, take a closer look at the script in that picture. It looks to be about twenty pages long... oh, and the pages are white. A full-length script is at least 120 pages long, and let's be frank: there is no way Warner Bros. would allow a copy of the script of one of the most anticipated movies of the next couple of years out of their sight. Plus, copies that circulate to potential cast members are almost always printed on red paper, which makes bootleg Xeroxing impossible.
And what about that "based on" credit? When we first learned that the Man of Steel sequel would be a Batman/Superman pairing, Zack Snyder introduced the project with a reading from Frank Miller's The Dark Knight Returns:
“I want you to remember Clark, in all the years to come. In all your private moments. In all the years to come, my hand at your throat. I want you to remember, the one man who beat you.”
The filmmakers have stated that while Miller's seminal graphic novel series would inform the tone of Snyder's film, it would not be a direct adaptation. Thus, this credit really makes no sense, and neither does casting any kind of Robin, given the knowledge that Affleck's Batman would be older and wiser.
In fact, it's unlikely that we'll ever see Robin in the next string of Batman films - the introduction of the character in the '90s film series was the beginning of the end of that continuity, and with Warners eying a Justice League film down the line, there's just no room. It means losing Nightwing, who as the grown-up original Robin becomes an interesting character in his own right, but overall it's for the best.
Finally, with the white-hot outrage over Ben Affleck's casting now dialed back to a slow boil, would the studio really risk alienating nearly its entire fanbase by casting a pop singer whose juvenile, narcissistic offstage antics have made him almost universally reviled by anyone over the age of 15? Probably not. We'll await the Funny or Die video Bieber refers to... and if it does not feature a spoof of his potential casting as Robin, then we can start worrying.
Man of Steel 2/Batman vs. Superman will hit theaters July 17, 2015.
Source: Justin Bieber