What a great ending. Good for you for being prepared and kudos to them for stepping up and realizing they were wrong. I'm sure a lot of it had to do with your respectful approach. Just goes to show that great manners still go a long way.
Glad it worked out for you. If you need to put gravel down before the concrete trucks come, invite the Fire Marshall up the day you pour concrete so he can watch the trucks go in and out. I have a gravel driveway, and the concrete trucks never left a track going in and out. Hopefully it will ease his mind and show him you appreciate him being decent to work with.