What Superman said was a catalyst for change in a man who forgot what he was fighting for. Thematically, it's represented throughout the entire film, both visually and otherwise. The Bat-creature smashing through Martha's memorial and dragging Bruce into the darkness, even the opening of the film; "in the dream, they pull me towards the light; a beautiful lie." We see a man who becomes corrupted by the weapon he forged in the name of justice; disillusioned to the point that he can no longer tell the difference between himself and the criminals he hunts; a man so driven by obsession that he's willing to murder a man in cold blood just because he finds his very existence to be a threat.
I thought the Martha moment was beautifully done, because it portrayed Batman at his absolute worst, and, simultaneously, his most vulnerable. I love the way the fight scene reflects the internal conflict and it's resolution in the film. There he stands, clad entirely in black armor; effectively consumed, completely, by the Batman persona, and I love that, as Superman tries to get through to him, he chips away at the armor, to the point where you can see there's still enough left of Bruce Wayne to break free of this dark, vengeful thing, and it's serendipitous; it's mere chance that their mothers would have the same name, but it reminds him of everything he was fighting for, and everything he's forgotten, and, even, betrayed. I mean, you have to think of it in the context of love. Batman exists because a kid loved his parents and he missed them, but, gradually, it consumes him to the point where he does it more because he hates crime than that he loved his parents, and that's what makes that moment so poignant; it's even more thoughtful when you consider how it honors 75 years of history between the characters.
It's not just something they created from the movie, it's something that's always been there, and something they used to create a powerful connection.