The ONLY reason I could see this being a real issue and not a nutty neighbor is if the kid gets hurt.
If they are mowing the neighbors yard and come into yours and hit something, throwing it up and damaging property, or they get injured while on your property, you would be liable for all damages.
That being said, whoever called the cops is a nut case. I'd have brought the kid a coke.
Well in my neck of the woods, if I cut my yard, then I end up cutting a small portion of two of my neighbors yards as well... You see I need the area for a turn around or line up to keep my rows straight on re-entry. Never had an issue yet.
Maybe the neighbor is a racist, and didn't want the black kid on their yard at all, but if that is the case, then that is a dam shame.