Maybe the whole driving thing is kind of a metaphor for who is in control? Pardon me if I'm typing out some blasphemy, and certainly correct me if I'm wrong (I have, afterall, only seen the film once, which is, in and of itself, some type of heinous crime, I'm told), but there quite a few memorable scenes where a car and its driver are somewhat pivotal.
Most notable in my mind is the scene where Brendan is coughing up blood and Laura offers to drive him somewhere and he sort of delusionally refuses for some time. I can't bring up the details of this scene (where she offered to take him, where they ended up going, why he refused -- some pretty major details, so if you happen to recall and it totally messes up my half-baked theory here, please mention it), but assuming they (the details, that is) fit, it does seem like part of his hesitancy to accept her offer is prompted by the idea that he would be out of control and, as he is already rather physically vulnerable, he's just totally put off by the idea.
Or! Or what about the parking lot scene with Tug and Brendan, or the scene where Brendan is thrown in and out of the Pin's van? Both of them revolve to a certain extent around who is in control; the former, I think, might end with Tug kind of relinquishing some of his control, but man, I really need to see the film again, so I'm going to shut up right here before I start assuming some pretty big things.
The point is, maybe although the idea of the Pin driving strikes us as kind of odd, it's just there to suggest that it is the Pin who is in control (of Tug and of Laura) at this moment in the story.