Interestingly he mentions catching a TfL» service to West Ealing. The link he provides to the National Rail website suggests GWR▸ is the only participating TOC▸ but it hasn't been updated since February, so I wonder if it is valid?
It does list only GWR under "train operating companies", but doesn't actually say you can only use their trains - that item is under the general heading of "Prices & information", but not called a restriction.
It certainly does say the rover is valid to Greenford, and at West Ealing, a station GWR no longer serve from the main line apart from the Greenford shuttle's in and out moves. It also says the rover is valid at Acton Mian Line, a station GWR no longer serve except before 7 am and after 9 pm.
Whatever it means to say, it could be clearer.