When my wife was pregnant with my daughter, 22 years ago there was something in place because someone came to pick my wife up. I'll never forget it because he was pissed that my wife wouldn't walk 100 ft up the block so he didn't have to go into the neighborhood. Then when he saw she was 8 months pregnant he felt like an ass and was very apologetic.
I'm not sure what they had in place, whether it was through an organization or just a few nurse's husbands doing a good dead like Quadna did but there was something. It was probably done on the down-lo and once insurance companies found out about it probably got stopped.
So if this was to be done it could not involve the hospital specifically. It would have to be word of mouth through nurses friends and what not. That way all it would be (in the eyes of the hospital, lawyers, insurance companies...) was friends giving friends rides.