I cloned the uv map. On the surface, it seemed successful. The islands matched perfectly in shape. However, in reality, each vertex is arranged arbitrarily without any rules.
I would expect the cause of this to be a different vertex ordering between the source and destination meshes used for the transfer.
In order to transfer UV, Blender needs a correspondence; it uses vertex order. The first corner gets the UV of the first corner, the second of the second, and so on, until it's done.
Many import and export functions can re-order UV. Some of these have options to control UV re-ordering. Inconsistent ordering of UV will create meshes that look that same but aren't really the same-- they don't have that correspondence that allows a UV transfer to work. A few Blender operations (not many, not frequently used) will also end up re-ordering vertices.
You could instead try a data transfer modifier to copy UV. Using a data transfer modifier, you can instead create that correspondence a number of ways; I'd first try creating it by nearest corner and best matching face normal. For meshes identical other than vertex order, this should work well.