One of our librarians just reported to me that she accidentally deleted one of our saved reports off the system. Her permissions were only set to "Execute reports" so this scenario should not be possible. It seems to be an unintended effect of incorporating the ability to delete multiple reports (bug #3134).
It would be nice to have a permissions setting for deleting reports.
Either a syspref for enabling the multiple reports feature or a permissions setting for deleting reports would work.
Deleting reports now has a separate permission: delete_reports
Please open a new bug report if there are any remaining issues!