I think the basic argument is that if the gutters were not blocked, rainwater from guttering would go down into the under-road drainage system directly, but if they are blocked, they go to the roads and add another burden to the already over- burdened road drains.
That seems to make sense to me, provided that water was not flowing up out of drain covers - which indicates excessive volume, too large for the drainage tunnels. This can happen, on June 30th, sometime in the 1980s, I remember a cloudburst when I was in St Aubin's. Driving up St Aubin's hill (I had to go through the Trafalgar because of the flood water), the force of water and the volume had pushed drainhole grids up in the lower sections of St Aubin's hill, and water was [ushing up out of them.