The Drive API has a Files.get method for getting metadata, including a modifiedTime field.
You can also save the last modified time within the spreadsheet itself using Google Apps Script by using an on change trigger. Try the DriveApp.getLastUpdated() method.
From the question:
Is there any way to tell Google Docs to not read this directory?
No. There is no setting for this on Google Documents, Google Drive, Google Account settings (Google help articles usually show what can be done, they very rarely include info about what can't be done and never include notes / warnings about "missing" settings ).
Adding a shared folder to your Drive with the Shift+Z shortcut only works if the owner of the folder has the advanced sharing option Editors can change permissions and share enabled. If this is disabled you'll get the unhelpful error message you encountered.
Steps to enable:
Login to Google Drive with the account that owns the shared folder
Locate the ...