The user order views' access permission is "View own orders of any type". I have given this permission to authenticated users yet the user sees only this message "You have not placed any orders with us yet.". What am I missing?
You've most likely edited the View to include a new relationship - perhaps from line items to products - that adds an access check to the View's results that the user doesn't pass. If this is the case, open your View's "Advanced" fieldset, edit the "Query settings", and check the box to "Disable SQL rewriting".