Resolution: When you define your workflow, there is a section "Post-completion Workflow Activities", where you can check "Update the approval status (use this workflow to control content approval)". If you check this option, and you do NOT have content approval enabled on the library level, you get the system account error message. If you do not check it, everything works fine.
Reason for occurrences: The account listed in the "User ID" column does not have permission to "something" that is being requested in the workflow code. Workflow usually running as the "system account" within SharePoint and should have access to all the objects within SharePoint. However, the system account may not have access to some resources that are outside of SharePoint and needed by the workflow code. Accessing outside resources is usually done via the .NET worker process account (e.g. NETWORK SERVICE).