Yes, that's the permission necessary for clearing the action log, and for deleting individual log entries.
Did you flush both permissions *and sessions* before testing?
Did you test from another browser where you're not logged into the Manager?
I've only flush permissions before testing.
Testing was in private session browser or from other browser.
Today I've repeat the test and flush both permissions and sessions, from another browser.
Results are the same - log was cleared.
Maybe I need to create a issue on github?
It does sound like a possible bug.
Thanks for reporting that.
