OK, I did a little more experimenting. It's a little more complicated than what I described. It's about FOLDERS.
Individual files are shared with no permission problems.
When my wife puts a document in a folder, the folder on her machine has rw privilege for her, r privilege for staff, and r privilege for everyone. When she puts that folder in my dropbox, it lands there with rw privilege for "nobody", r privilege for staff, and r privilege for everyone. I am unable to copy that folder out of my dropbox without changing permissions.
If I put a document in a folder, the folder on my machine has rw privilege for me, r privilege for staff, and r privilege for everyone. When I put that folder in her dropbox, it lands there with "custom" privilege for her, rw privilege for me, r privilege for staff, and r privilege for everyone. She is able to move it an manipulate it without changing permissions.
So why the asymmetry, and why don't I have permission to manipulate a folder she puts in my dropbox?
Now, it is true that on her machine, I am listed in "sharing". On my machine she presently is not. If I specify on my machine that I want to share her dropbox, and list her as a user, maybe that will fix everything. But why does this have anything to do with dropboxes??? I am not accessing the non-public part of her machine directly, and she is not accessing mine directly.