My apologies, I saw the fare and didn't look at the available trains.

You are right. thetrainline based booking engines aren't showing the SSR as valid on the services via the Berks & Hants.
An error obviously. My suggestion, book via a WebTIS based booking engine or at a station. Oh, and let
FGW▸ know that you can't buy the ticket through their website.
Or, if seat reservations aren't important, book via FGW choosing available services and just travel on the 1019 or 1119. The SSR is perfectly valid on those trains.