No, no, no, you guys got it all wrong. Batman has only been publicly operating for 5 years, but he existed before then (according to the JL origin reboot). The fact that he was an urban legend prior to his coming-out allows for any time-lines since it becomes unclear when he actually started working.
He's been operating for 7 years after the Justice League was formed, and maybe 1 or 2 years before that.
Batman: Zero Year takes place a year before Justice League: Origin, so Batman had only been active a year before the Justice League formed in the New 52. Though Bruce Wayne was active in Gotham months before he became Batman, he was simply an unnamed vigilante during that time. So it could be argued that he built up his "urban legend" status during this time, and later after he became Batman people began to become more aware of him, mainly because he was suppose to be a symbol to the people of Gotham, which thus required them to know of his existence.
This would also explain Green Lantern's reaction of Batman in the first issue of Justice League, as while Batman may have been known to the people of Gotham, he may have still been an "urban legend" to people outside of Gotham, such as Hal.