I am not an attorney but am speaking as homeowner on a private road with a culvert that drains a part of my property into a commonly used private ROW that is the responsibility of our statutory road association. I recently paid to have my culvert reset within the ROW at the same time the association was paying for the completion of other road maintenance.
I suggest having owners maintain culverts that primarily benefit their properties whether on not these culverts are within the boundaries of the private road. If culverts under driveways are part of the ditching to drain the private road then the association pays for maintenance.
Try to keep attorneys out of these decisions. This should help matters remain low-key. Attempt to find a solution that is fair and equitable to all parties.