The problem is defining a seperate Proxy Custom Directory. Blender should make unique folders for each strip in the new folder path, but doesn't. Instead of creating new folders it just renders proxies over each other in the same place. Perhaps it is not a bug, but I don't understand why you can define a directory that you cannot use.

Proxies work as expected if they are colocated in the source footage directory using Proxy Custom File option. But I wanted to render them somewhere else.

It would seem that when using Proxy Custom Directory, the user must set up a folder structure for each shot and define the folder for use on a per shot basis. If there are many many shots this is very labour intensive. Prefered method would be to define one folder and let Blender create sub-folders for each shot.

Sorry for the trouble, it seems to be a feature but I couldn't find docs for it.

Findings:
1. The option Proxy Custom Directory allows you to render image sequences for meta strips and scene strips into a single folder. They automatically have unique image names so seperate folders don't need to be generated by Blender.

2. The option Proxy Custom File allows you to render seperate jpeg movies for each movie strip, in this case Blender will generate a unique folder for each strip.

If you accidently reverse the selection Blender will write the movie strip proxy files over each other.

Suggestion:
I feel that the user should not be able to select Proxy Custom Directory for movie strip proxies. as that doesn't work correctly.

AFAIR, custom proxy file was keept for compatibility reasons and currently custom directory is better to be used.
And indeed i defines directory to where all proxy-related files would be stored and where there'll be no additional folder structure be created. It is possible to make it's smarter to be able to use the same custom folder for all strips, but it's not actually easy because you might have strips which are using movies with the same name from the different locations (so name-based proxy directory creation wouldn't work). Other approaches makes it's complicated to re-use proxies from different .blend files (because that unique part of folder would be .blend file dependend).
I'd wouldn't consider this is a bug.
P.S. It is possible to write simple python script which will set proxies folder for all strips in a way <some given prefix>/<movie file name>.