Additional permissions are required to access the files (Word for Mac)

This is a fix, but the specific steps are a bit drastic by removing your whole keychain, which contains a lot of other useful things.

You can fix this in a different way without messing up your whole keychain.

Make sure the office Applications are closed.

Within KeyChain Access, just search for ADAL, remove the entries starting with 

MicrosoftOffice as the kind plus com.microsoft.adalcache

The 16.27 update release July 16 2019 should fix most of the issues with this Bug.

Additionally the following are some fixes that will fix this specific error and similar permission errors with Office Mac products

1. Update Office to 16.27 or later (choose Check For Update from the Help menu in any Office Application)
2. Remove Microsoft ADAL keychain entries (search for ADAL in the keychain and remove those items)
3. Remove the securebookmarks preference files

Press Command+Shift+G in the finder then paste the following

~/Library/Containers/com.microsoft.Excel/Data/Library/Preferences/

Within this folder remove the following file

com.microsoft.Excel.securebookmarks.plist

Press Command+Shift+G again and then paste in the following

~/Library/Containers/com.microsoft.Word/Data/Library/Preferences/

Within this folder remove the following file

com.microsoft.Word.securebookmarks.plist

After any and all of the above steps, please reboot your machine (manually removing preferences and keychain items does not guarantee they will be recreated properly unless you restart)

Additionally if the files are located on a shared drive, the files may be open by someone else. The other users may also just have the files highlighted in the finder (whereby it is then generating a preview of the file and therefore the file is marked as open)