He's been busted on this in a number of other episodes as well, I'm sure someone else can provide a full list if there's really a need.
It was just a plot device for that single episode they didn't really think through coupled with the human imperfection of both the actor using one by reflex and not thinking about it and the director and staff hearing one and by reflex not thinking anything of it.
It would've been funny if they pulled something like in Armageddon Game. Where Keiko sees a video of O'Brien's death and realizes it must be faked because he never drinks coffee in the afternoon. Well of course it was faked, but O'brien revealed at the end he did drink coffee in the afternoon and he was saved over a false assumption.
