I discovered the problem folks. You must have an ORGANIZATIONAL account to have a hosted service show up in your publishing process and to be able to publish like we are talking here. I had a PERSONAL account which has limited abilities. If you have bought and paid for an ESRI license, you are entitled to a free Organizational account. In order for that to be set up you have to call ESRI customer support. They will send you an email enabling you to set up an Organization account, which has the appropriate rights to do what we're talking about. In other words, when you log into ArcGIS online, if you don't have a tab the says "My Organization", you don't have an organizational account.
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