Accident or not, when damage is done to somebody's property, the property owner is legally entitled to reparations.
Not from "Their" insurance but from "Yours",, or cash will do just as well if you don't wanna get the insurance companies involved.
The alternative is of course small claims court, but in Your case if you're actually going to dispute the claim simply because it was an accident I suggest being Prepared to LOOSE!
Haven't you ever seen Judge Judy?
Just PAY and be grateful that your neighbors were reasonable enough to not call the police & press charges since in most suburban jurisdictions even firing a dumb BB gun in one's own back yard is Illegal as hell!
Trust me I've been there!
All it takes is a pissed-off neighbor to tell a 911 operator that their window was 'SHOT' with a bb-"GUN" and the cops can definitely respond with More than just One car and make a damned embarrassing viral-worthy spectacle of everything!
And being a SmartaSS to cops about it wont get you anything but your yard decorated with Crime-scene tape , cuffed & seated in the back-o-one of those cars while Cops talk it over with Parents for a few hours,
and with the "Least" of your problems, having to pay for a stupid window & totally kissing your BB gun goodbye!