Isn't the story that the script he was given was to say "one small step for a man", but on the day he flubbed his line and actually did say "one small step for man"

He wrote those words himself, and he's always claimed that he actually said "a" and the mic didn't pick it up.

It's been the subject of some technical analysis over the years: http://news.bbc.co.uk/2/hi/science/nature/8081817.stm

NASA trusted those guys enough to give them carte blanche with stuff like that, which is why Pete Conrad said "Whoopie! Man, that may have been a small one for Neil, but that's a long one for me" in order to win a bet (and because it was funny).