I believe that the original Chado creators were assuming that the binomial name would be deconstructed when stored in the organism table.
e.g. genus = 'Solanum' and species = 'lycopersicum'
The constraint then enforces the uniqueness of the scientific name (genus + species). This makes complete sense from a database design point of view in terms of reducing redundancy. It is less clear from the biological point of view and I could see where it might lead to different interpretations.
At FlyBase we follow the genus = 'Solanum' and species = 'lycopersicum' model.