My understanding is that the Post Office directories are generally based on the proper historic counties, not on districts or areas or regions or postcodes, all of which are more recent inventions. Until TPTB messed around with the local authority boundaries in the 1970s, the county was always part of any postal address.
So Avonbridge, being partly in the parish of Muiravonside and partly in the parish of Slamannan, will be listed, if it is listed at all, in Stirlingshire.
It may be that the compilers didn't bother with smaller villages and hamlets.