Nothing to stop you claiming direct from his insurance company, although if it is just a wheel true, then it hardly seems worth the bother.
The insurance company can either say yes or no, but you have nothing (further) to lose.
There's a small point that might go in your favour.
Was the kerb 'dropped' where he reversed over it?
Many house driveways of this type have simply been established by the house owner by use - they have no legal standing.
So it may be that he shouldn't have been reversing - or going forwards - where he was.
If the kerb is 'dropped' then the chances are it's a proper driveway.
But if it's not, then it may not be a proper driveway which, as I say, is a small point in your favour.