I can't ever remember my DM taking or collecting me from school - I just went with all the other kids. I remember taking my DSis in her pushchair into town when she was a toddler (so I would be 6/7). She got out in M&S, fell over and cut her lip: they took us into the stockrooms and gave DSis a book to quieten her down. We had a canal at the end of our street, we were always up there fishing and, of course, occasionally fell in - someone just pulled us out!
DH and one of his school friends were reminiscing about going up on the moors to play - friend's DM hung a sheet out of the window when it was time to come home for dinner. They also once let a fire get out of control on the moors, but found a phone box and rang the Fire Brigade to come and put it out.
I think the thing is that obviously things did happen, but there wasn't 24 hour news coverage so people didn't fixate on things. I do think that it might depend on where you live: when we moved up here the DC suddenly had more freedom. Also you must remember that during my childhood people rarely had phones, so our parents mostly trusted the wider community, and, of course, people tended to mostly stay where they were born so everyone knew everyone else.
BD, good luck with tomorrow.