But often, fences are not on 'your own property'.
When streets of houses are built by a developer they will generally have identical deeds. (This is an estate of 40 private houses built by a developer 30 years ago). If there are 'T' marks on the plans then yes, that indicates who the boundary wall or fence belongs to. The deeds make it clear enough, as they did in our case, (joint responsibility to maintain). Without checking the deeds, householders may often make mistaken assumptions. I've no doubt in my case, the neighbour had an honest but mistaken belief that the fence was hers to do with as she wished. She is now better informed.
As to whether or not she sought legal advice, I've no idea, but I did, as I did when a wild cherry that she'd planted within a metre of the boundary fence and two metres from our brick garage and greenhouse fifteen years ago, had grown to such proportions (already 40 feet high, and still immature) that it was overhanging our property and the roots were disturbing our patio slabs and undermining our brick greenhouse foundations. I obtained an arboriculturist report which indicated that it was the wrong tree in the wrong place and the only way to abate the nuisance was for it to be felled. Fortunately I have free legal cover on my house insurance, and she was given notice by lawyers that unless she removed the tree within 28 days a civil action to abate the nuisance would ensure and would proceed to court. The tree was duly felled.
It also states in our deeds that the front gardens must retain an 'open aspect, with no hedges or fences'. However, at the front of her garden adjacent to the pavement, some years ago she planted a laurel hedge which is now 14 ft high and 6ft deep, overhanging the pavement. Not a matter of concern for me, but it is for the Local Authority as the hedge is obstructing the pavement (classed as part of the Highway).
It would be quite wrong for me to refer to her as a 'nightmare neighbour' as she's rarely to be seen. She is simply reclusive, estranged from all other neighbours, has venetian blinds at every widow which are always closed.
All I'm saying is that it makes sense (to me anyway), to not make assumptions about who owns what, but to check the deeds. Where life does get complicated with boundary disputes, is that the the lines on the plans do not indicate with total precision exactly where the boundary is, which is why boundary disputes so often escalate over a 15cm strip.
In conclusion, I didn't think the fence in the first post of this thread looked too bad. Much better than a dilapidated one. But it seems to me that both the OP and his neighbour have an honest belief that it's the neighbour's fence to do with as they wish. That might be so - it might not.
In a troubled world, it makes sense for neighbours to try to get along together as best they're able.