This is a strange one. It looks like the default route has been suppressed as the fare finder is only showing the via Putney/East Putney fare. This shouldn’t happen. There will be a default route set, which is probably zone 1-3 as you predict. I’m not sure whether via Clapham Junction and West Brompton would also trigger an alternative. You might need to touch both pink readers.
In general, alternative routes are shown wherever they are set up. It’s certainly not just for avoiding zone 1.