For some stations, this is a bit of a grey area. However, in the case of Westbury I think you would have trouble convincing anyone that the avoiding line is part of Westbury station. Looking at the
train, Westbury isn't even listed as a timing point.
Luckily, you don't have to in this case. If you say the avoiding line is not part of Westbury station, you reason as follows:
An off peak return between Reading and Westbury is valid for break of journey anywhere along a valid route.
WE is a valid map for a journey from Reading to Westbury (and vice versa).
This allows the journey Reading Group-Newbury-Westbury Group.
If someone was to travel between Newbury and Westbury Group following this map without doubling back through any stations or passing through a station which is a routeing point, or part of one, en route, there are a number of ways to do it.
Newbury-...-Pewsey-Westbury
Newbury-...-Pewsey-Frome-Wesbury
Newbury-...-Pewsey-Frome-Bruton-Westbury
Newbury-...-Pewsey-Bruton-Westbury
Newbury-...-Pewsey-Bruton-Frome-Westbury
I haven't checked that there are trains you could use for all of these journeys. My point is that you can switch to the rover as your train passes through Bruton, and not worry about any of this.
If, on the other hand, you assert that a train which uses the avoiding line passes through Westbury station, you can switch from one to the other there.
The only set of assumptions I can see on which you would have a problem would be if you assert that Westbury station includes the avoiding line for some purposes, but not others. I can't think why anyone would do this, though.