If you run your farm on least privilege settings, you can get the above error.
Be aware of the security demand for the Word Viewing Service are quite high:
When you create a new application pool, you can specify a security
account that is used by the application pool to be either a predefined
Network Service account or a managed account. The account must have
db_datareader, db_datawriter, and execute permissions for the content
databases and the SharePoint configuration database, and be assigned
to the db_owner role for the content databases. For more information
about services account permissions in SharePoint 2010 Products, see
Account permissions and security settings (SharePoint Server 2010).
So basically that means that the Web Service Application Pool needs to have db_owner permissions on each content database, which a normal service application pool should not have.
To test if this is the case, try temporarily to set the farm account as managed account for your Web Service Application, do an IISRESET and see if that fixes the case (note that you should only do this as a temporary exercise to find out if this is in fact why it fails).