Heck, that happened in my area of CA in the 1980s and '90s. Because of things like : A) redneck aggie punk kids who used to go at night & spin donuts on the lawn with their 4WD's, B) perverts who hung around schools ? C) dingbats who might fall off the monkey-bars or swing set and sue the school.
Nothing at all to do with md'ing. And to this day, there's usually always still a propped open turn-style, with a faded obligatory sign next to it that says something like "visitors check in at office" (that no one reads or pays attention to). And there's still dog-walkers, persons who jog the track shoot hoops, etc...
And I'll bet that if those dog-walkers or joggers went and asked "can I?", they would be told "no". Then they too could start forums lamenting their lack of freedoms