Basically you are correct. Back of house, existing rool level not exceeded, Less than 40 sq m, back garden not then less than 25 sq m, no windows facing neighbour and you are exempt.
When you are exempt you are exempt.(full stop) There is very little if anything the neighbour can do except fall out with you and steal your bin tags.
If when you tell them they kick up a fuss just apply for permission for the extension or I think there is a provision that you can apply to the council for a certificate that it is exempt.