On an alternate Earth, the normal Batman saved the life of that world's Thomas Wayne. That world's Bruce still became Batman.
AND in a JLA story that had to do with Synchronicity - Bruce's parents never died and that erased "Batman" from the present time (until everything was solved). If his parent's wouldn't of died, he wouldn't of been Batman - it's as simple as that. Nearly every comic mentions or starts off with what happened to him/his parents.
Peter was already Spiderman - what he chose to do with his powers was up to him, but he was already spiderman. Same thing for Matt Murdock, eventhough I'd say he became DD b/c of that reason more than Parker became Spidey for "Uncle Ben"....