My kids’ old preschool must have read Freakonomics and instead charged $5/min. My wife once fell asleep and was charged $90 for being 18 min late (I got a call at 6). At least it wasn’t $5/min/kid (2 kids).
Mostly, if parents were running late, they’d ask another parent to check out their kid and watch them for a few.
https://freakonomics.com/2013/10/what-makes-people-do-what-t...
In any case, it’s not just a story, it is described in this paper:
https://rady.ucsd.edu/faculty/directory/gneezy/pub/docs/fine...
I’ve read about the daycare fines before and didn’t have reason to doubt it any more or less than other anecdotes I’ve read. The paper you linked seems like pretty good evidence that it actually happened — assuming the rest of the paper supports the abstract.