From The Cambridge Grammar of the English Language, page 519:
Genitives, such as Christ’s in [4iv], we take to be modifiers not determiners. They occur readily in names that are themselves functioning as modifier within a larger construction, as in a Christ’s College don: this is a construction which accepts nominals but not full NPs in modifier position. Such genitives cannot normally contain a determiner — compare King’s College, Women’s College, etc.
I don’t see what is the clear difference between modifiers and determiners. Aren’t the latter just included in the modifiers’ category?