Just report it for the sake of reporting it, the fact that the van drove off and company dodged them is usually enough for the companies insurance provider to pay up. You would only report it to your insurance provider so they contact the other company to sort it out through official channels. If for some reason the other company does not pay up and no fault is found, then the neighbor can just say he will pay it himself and not claim it on his own insurance.
Usually if this was a parked car, you would report it to the police, get a reference and then give the reference to your insurance provider. I did a similar thing when a car hit a brick wall and drove off. In the end the culprit was not found, so we paid for the wall to be done rather than claim.
The reason why you report these things is just so it goes through official channels.
what do you even mean by that - we're talking about reporting it to an insurance company here not the police right?
it seems utterly pointless if you're then expecting the insurance company to demand money from the company that owns the van - there isn't anything inherently more 'official' than the neighbour doing that himself and you've seemingly ignored the point about premiums