"Copy" Activity, to and from the same folder in Azure DataLake doesn't work

I need to rename a file, in an Azure DataLake.
Since there's no "Rename" activity (which would be nice, :bats_eyelids:) I create a Copy activity set up with:

Source: `MyLake\Path\File.txt`
Destination: `MyLake\Path\NewFileName.txt`
Delete after Copy: `true`

When I run this, either in Debug mode or after Publishing, it reports success, but hasn't actually done anything. Neither the new file is created, nor the old one deleted. Viewing the Source & Destination UserProps of the activity in Published Activity run details confirms that everything is superficially correct.

If my targets are 2 _different_ folders within the same DataLake, then it's fine. Indeed, if I chain 2 copy activities together sending `Path\File.txt` to `NewPath\File.txt` and then `NewPath\File.txt` to `Path\NewFileName.txt` then _that_ works. It's only if the Paths are in the same folder that it breaks.
Similarly, the same code, but using FileShare datasets, rather than Azure Data Lake datasets, works just fine.

FWIW I've tried having separate (but identical) Datasets & Linked Services to define the Source & Sink ... no effect.