They are, because they don't look good at all, no matter how you incorprate them. Ok, I thought I knew how to reply to that... but... ...I just think you have a lot to learn and a lot of getting-rid to do.
Well d'uh, there weren't any wires back then. As you say, it was a great time to be a gangster, because investigation technologies weren't really there yet. So they did the only reasonable thing and had several guys in hearing distance to testify to Gillian's confession. And they actually tried to make her confess before, when that one "friend" of Roger approached them in the restaurant.