That is related to what Teddy was alluding to. If you have no unique identifiers then you have no primary key and you also cannot have any relationships which means there is no relational integrity. That means you don't have a relational database.
Access won't write to a linked table (or use a linked table in an update query) until it is assured that each record will be unique hence the request for a unique key. I really wouldn't advise that you rely on your FE to enforce uniqueness and in any case there is no RI with this setup.