Laurent,
Good question. The tongue morphology is new information for us. Can you provide a reference?
The taxonomic conclusion is derived from Fjeldså et al. 2020 who treat it as a subfamily of Motacillidae, Carpospizinae (see p. 63). It's a deep phylogenetic divergence (see Figure 14.2, p. 264), similar to that of Hypocryptadius within Passeridae, which they treat as a subfamily, too. Jim's suggestion that Carpospiza may deserve its own family should not be taken lightly (as could, arguably, Cinnamon Ibon).
Presumably, the phylogenetic study that Fjeldså et al. reference to help support their placement of this species in their phylogeny is Oliveros et al. 2019, but I can't find that taxon anywhere in that paper. Perhaps this data is buried deep in one of the appendices?
So, we're depending entirely on the conclusions of Fjeldså et al. 2020 for this conclusion.
David