First, thanks for both responding!
To answer the questions you both bring up:
It does need to be done programmatically, this is for picking a folder from within a running UI.
The Files sheet UI definitely seems to be able to pick a folder...at least, I've seen other apps use it for that purpose. Even pythonista itself can select a folder from the Files sheet for import and other things.
If it's just that pick_document() is restricted to only picking files, and cannot pick folders, that's what I'd want to know.