I'm confused about this. The Hispaniolan solenodon is one of those species that is rarely seen and LC seems a very optimistic assessment, especially as some 'critically endangered' species have populations of tens of thousands.
There are certainly species with still pretty high populations assessed as CR - such as the hamster discussed here, or European Eel - in these cases my understanding is it's because the rate of change of the population is so high that action is needed.
For what it's worth, this is the justification for the solenodon:
This species is assessed as Least Concern because it has a large extent of occurrence (EOO) of approximately 80,493 km² and is found in numerous protected areas. Whilst there is ongoing habitat destruction and degradation across several parts of its range, there is no evidence of recent subpopulation declines or extirpations. It may qualify as threatened in the future if further data show that habitat loss or predation by invasive mammals are significant threats.
Solenodon paradoxus (Hispaniolan Solenodon) (iucnredlist.org)