Hi -- are you using a data connection to the UpdateListItems method? Can you access other SharePoint web services from InfoPath browser forms in your environment (try with OData or you could use the CheckOutFile method - it is pretty simple).
If you are using a data connection, the field you are using for the list name parameter can't have a namespace (or at least this was the case when I first started using this method w/ ShP 2010 -- namespace on the node would cause the submit to fail). But since your error is an unauthorized, I'm wondering if something in your enviro is preventing web service method access from browser forms.