To me, this is simple. Let's say you lost your ATM card, and "Woman X" has found it. She's figured out your pin, but you only have so much in checking. It seems innocent for her to pretend she's you and want to transfer money for savings to checking, so she has easy access to it from an anonymous ATM.
I know things like this seem like long shots, but it happens every day. People with even average computer skills are hacking their way into our personal lives and obtaining all the need to steal our identities.
I'd much rather be safe than sorry. So what that you had to show your picture ID? They were doing it for YOUR benefit. I don't think that makes it more difficult to use your account...me, for example, if I'm out of the house I always have my ID on me...so what's a few seconds to reach in and pull it out?