Can they be opened if they are saved to disk first? I am asking just to help
diagnose the problem. If it cannot be opened after it is saved to disk, can
the same file be opened by other accounts?

Strange: If I rename on the desktop the currently saved example.mht to
example.mhtml it can be opened, too. If I copy exaple.mhtml to
example2.mhtml, the error message appears.

I didn't see any ACL differences.
Perhaps trouble with alternate data streams?