The 'rule' about fence posts, not sure of it's legal status, but it is certainly accepted practice. The owner of the fence has the posts on his side.
The 'pretty' side is for the outside.
If a fence is erected back to front, then either you could ask for it to be changed, or as it would appear to now be your fence, you change it yourself !
If you look down a row of terraced gardens you should see that all the fence posts are on the same side, typically all the fences on the right are owned by the house, fences on the left are next doors