The school cop may have been a semi-competent official responding to a somewhat legitimate complaint.
But,if you are an innocent party unconnected to the incident in question,then you aren't included among those with a "need to know" about the particulars of the case.
It sounds as if his best shot was getting you to incriminate yourself or revealing some confirming evidence in plain sight.
He might have been plain out of his league in investigating a possible stalking,terrorist threat,burgulary or vandalism threat,etc.
(Of course,if he were lucky,you could have confessed that you were a recovering pedophile and driving by empty schoolyards was your way of "cutting down.")
I once had someone accuse me of planting a bomb under a friend's car while he was in Nashville.
(At this time,I had no transportation to Nashville.
I don't think my church friends or the Senior Bus would have
given me a ride so I could murder a federal employee.)
The authorities had to look into it even though the tipster
wouldn't give a name.
Nor would they give a time or place of the alleged crime.
"If I tell you when she did it,she'll just give you an alibi."
DUHHHHH
.
Heaven forbid that I be in the hospital,on jury duty,
performing in a play or at a bank or grocery store or restaurant that could provide witnesses,security cameras or time-stamps to confirm my whereabouts.
The informer had a certain lack of credibility but the powers-that-be had to determine whether there was a smoking gun or if the caller was trying to share their personal stash of hallucenogens with the agents' backsides.
As Bernard Fife might have said:
"It is better to arrest the harmless,lonely stranger who knows too much about folks in the community than to barbeque a goat that has devoured a shed full of dynamite."