That would explain it; it wasn't unheard of for some proteges to take on their mentors mantles. And if this guy was sixty years into her future, it would explain why she had absolutely no idea who he was. If he even was who he said he was.
"So that would make Batman..." Really, really old. "Come to think of it, I don't even know how old he is. I remember he was a few years' younger than my dad...I think...but that's it."