Why do Permissions say "Fetching..."?

For many -- perhaps most -- of my files and folders, the Get Info (Command - I) window shows a greyed-out "Fetching..." for the name of the only entity with Read-and-Write privileges:

What does that mean?

Perhaps relatedly, iTunes will not run, complaining via an alert box on launch that

The iTunes Library file is locked, or on a locked disk, or you do

not have write permission for the file.

Clicking OK on the alert box Quits iTunes.

I tried changing the enclosing "iTunes" folder's permissions

to add (Me) with Read and Write privileges.

I then deleted the "Fetching..." entry.

Then I selected "Apply to enclosed items" from the gear icon.

This new pattern did not propagate to the enclosed items. (I checked several.)

How is this supposed to work?

--Gil