Where on a fence do you measure?
It depends on what the client wants, and the specific circumstance(s).
This situation doesn't happen much where I work, and when I does, I try to explain why that is not such a good idea for the client moving forward. However failing that, I ask the client to set stakes where they expect the corners to be and I will measure to them and perpetuate that with a more permanent point and the words to memorialize it. We discuss ownership and maintenance responsibilities in advance.
It saddens me when I see fences located to the nearest 0.01' on a survey. I measure to the center of the post and qualify that to be within 0.1' of its relative position.
If a physical boundary legally establishes a straight section line then the line is straight in a legal sense although not in a measured sense.
As usual, it depends.
But in absence of any other indication...
Where the rails meet the posts.
That way half the fence falls either side of the boundary.
Urban: centre of fence rail for side and rear, road side face for front.
Rural: along the line of the wire.