Why Do I Get "Detail: Not Found" When Trying to Download My Job Stdout?

Issue

When attempting to download a job's output (i.e. Download Output in the Tower UI), you may run into the following error:

{
    "detail": "not found"
}

/var/log/tower/tower.log may also report this:

OSError: [Errno 13] Permission denied: '/var/lib/awx/job_status/job-123658-XFsfEf.out'
2019-07-15 13:26:59,426 WARNING  django.request Not Found: /api/v2/jobs/123658/stdout/