The API documentation here is missing ‘section’ and ‘subgenus’ from the ‘rank’ drop-down menus:
https://api.inaturalist.org/v1/docs/#!/Taxa/get_taxa
https://api.inaturalist.org/v1/docs/#!/Taxa/get_taxa_autocomplete
I was working from these menus as an authoritative list of what the rank argument would accept, causing me to miss both of these ranks in the code. However, I found experimentally that the API honours both keywords, matching records for them when specified.