Sounds more like a frightened woman was further frightened by a bloke turning up when she was vulnerable and saying
'I can stay with you' - um, no. 'In my car' - not getting in your car with you.
'You can come back to my house, I'm just around the corner' - no.
'You can stand in my driveway' - still not going with you to your house.
'My wife asked me to help you' - how do I know that? You could have seen me here and decided to take the opportunity.
'This is my name and address' - does that make getting in your car as a strange man inviting me back to your house any safer when it could easily be a false name and address?
Just because he meant 'I'm going to rescue you and although you haven't a scooby whether I'm doing this for altruistic reasons or so you feature in a documentary in nine years about how you disappeared from a broken down vehicle and was never seen again but a piece of paper with a false name and address was found at the scene, I'm definitely doing this because I'm a latter day Knightrider' doesn't mean that she was going to instinctively know that going against everything women learn about how dangerous men can be would be fine on this occasion.
All the advice for women in the event of a breakdown that isn't on a motorway is to stay in the car, to not accept help from strangers (specifically men) and to report if somebody (specifically men) make you feel uncomfortable. And that a genuinely benign person - man - won't be offended.