Got the message back from task scheduler:
An error has occurred while attempting to set the task account information. The specific error is:
0x80070520: A specified logon session does not exist. It may already have been terminated.
However, I am logged in and can run a SQl query.
That explained it. Thanks. We will probably leave the local network access setting enabled to not allow storage of passwords and credentials. That way users can build and test automation jobs but when it is ready for production (and to be scheduled) they will have to request to put it on the server ensuring following the development to production rules, change control, etc. are followed. We will only disable that setting on the server, if needed.