The CV is no longer trained on the genus if it has learned any species in that genus – that is, the training set does not include photos of observations with a genus level ID or observations of other species within the genus that don’t yet meet the criteria for inclusion themselves. Material used in previous iterations of the training does not seem to be carried over (it does not “remember” out-dated information).
However, as I understand it, it is provided with some information about taxonomic hierarchies so that it can compare relatedness of the taxa in its training set when making suggestions. For the website and the old versions of the app, the top CV suggestion is deliberately always something higher than species. But when it makes these more general suggestions, it is not because it knows the genus per se, but because it knows a particular species and knows the species is in that genus.
If the CV only knows a few species in the genus, but these species are more-or-less typical representatives of the genus, this would not be a major issue – it would suggest the correct genus even for observations of species it has not learned. But when the only species that are identifiable are atypical representatives of the genus, it does not recognize typical members of the genus because they do not resemble the material it has been trained on.