You are wrong...
Thames Rover is available at a number of stations served only by
SWT▸ , eg between Reading and Wokingham. They should be familiar with it at any station on it's validity map, such as at Banbury (Chiltern).
(
BTW▸ , according to the
NR» rovers and rangers pages, the tickets in the relevant area are known as Thames Rover (3 day or 7 day), and the Thames Branches Day Ranger - the latter would clearly be an '
FGW▸ only' product.)
Paul