Depends on which identity he was counting on to have been destroyed.

Julian tilts his head--of course Captain Kirk was famous, but he didn't think--with the anger there in his voice, which made sense with his boast of the Enterprise being a wreck, and the fact that he attacked an Ensign, Julian didn't think Kirk would have been one of this man's first concerns.

"He was killed in action on the maiden voyage of the Enterprise-B in 2293." Presumed, because he actually hadn't been. But that would be calling on knowledge that wouldn't become commonplace until a few years from now.