Yep you are right, technically you are not allowed to paint or fix anything to the the side (facing your yard) of your neighbours boundary wall.
Knowing this I actually consulted my neighbours and selected limestone face bricks for my garages. My house and garages will be rendered inside and out on all walls except those on the neighbours side.
One neighbour also has a boundary wall on the same fence line as I have my rear garage and we are both having limestone bricks and have verbally agreed to allow each other to render to the same colour scheme.
Its not worth arguing over because boundary walls are allowed and it is approved. Best is to accept it and discuss with your neighbour about rendering or painting. To be honest it also protects the wall I would have thought.
Boundary walls on the boundary are more expensive as the gutters have to be contained within the fence line which costs a lot more than normal gutters.