The primacy of consciousness is evident in their theory. They may start with the beliefs of people in general to determine which candidates there are for true propositions that could justifiedly be accepted as true, or they may single out their own beliefs as the best candidates. A belief in what you do not know cannot be justified at all. If you are justified in holding something as true, then it is becase you have adhered to the methods of logic in differentiating and integrating the information provided to you by your senses and in your higher level abstractions. Nor could a belief in what you do not know be true.
Truth is a recognition of reality.
If you have reached a belief that does not correspond to reality in a fully proper way through your own thinking, then what you have is neither true nor knowledge. This is what modern philosophers start with the arbitrary, any belief. By adding these qualifiers they still don't have a clue to what knowledge really is. They only know some features of what is often regarded as knowledge by people. In this way they avoid looking at reality.