And where do you get that from? At most Batman would have been this so-called urban legend for maybe 5 years, if that.
This board has known for a year that Batman had been an urban legend for a long time in the MoSverse. It's an inevitable consequence of other pieces of information officially confirmed.
At the time of MoS, Superman is the only publicly acknowledged superhero, which Snyder and co have said many times. It was understood when it was announced that MoS would lead to an expanded DCCU that Superman would lead/found the justice league, either by recruiting new superheroes or joining forces with other heroes who have been operating in the shadows. Perhaps Wonder Woman has been secretly active for thousands of years.
When Ben Affleck was announced as Batman, we knew he would be in his mid 30s at a minimum and probably mid 40s. When it was said that he was tired and weary, we knew that he was a long-time veteran. Coupled with the fact that Superman is the first superhero operating out of the shadows, that leaves only one conclusion: Batman has been operating in the shadows. If he's in his mid 40s now and started at age 25 (reasonable), then he's been an urban legend for decades.
Everything I've said thus far is foolproof and beyond rational debate.
Everything I say following is speculation.
Batman is an urban legend within Gotham but significant parts of the police force, local government and possibly state government are aware of him. He chooses to remain an urban legend because the ambiguity of whether or not he exists makes him more frightening to criminals. They don't know if he's real, if there's one Batman or many Batmen, if he's a man or something else. They're scared, and Wayne likes it that way, he only cares about bringing fear to criminals. It also helps law enforcement because Batman can do the things they can't. However, after a few decades of this and several beatings, he slowly became bored and less interested, and further the progress he made in Gotham with Batman, though initially strong, stagnated with time. Gotham has reached a new equilibrium even with Batman and things have stopped improving.
Here comes news of this alien invasion. Batman had not made it to Metropolis on time before things were solved by the alien, whom Batman doesn't know if he should trust. He investigates the hero, confronts him, and they reach a cold truce. There's a new conflict that emerges, [insert plot of movie here], Superman ends up convincing Batman that rather than trying to strike fear into the hearts of criminals, he should bring hope to the hearts of the general population, that it's the next step in improving Gotham and Metropolis and the world, and that involves coming out in the open. Together, they found the Justice League.