Well, I'm not sure I would buy straight out that he did not mean to fashion his characters after Bible characters. I think to argue that he meant there to be an exact, one to one relationship for every character would certainly be a distortion. But on the other hand, biblical types, or archetypes are clearly in play in his stories. I am not saying it is necessary to see that each Narnian character represents a single biblical one (except for Aslan), but combinations of these archetypes are obviously in the mix.
Josiah himself, though an historical king, is highly archetypal. Anytime you get descriptions like those that describe him (purest, holiest, most sincere, etc.), that's archetype. The same applies to David and Solomon, who become larger than life characters in the Bible. These archetypes are realities that float around and are tapped into by story tellers. If I tell you a story about a young princess, kidnapped and held by a dragon, then rescued by a young knight who kills the dragon then marries her, well, that's me tapping into a bunch of archetypes. I reference things both consciously and unconsciously when I choose to tell such a story.
So, do I think that there is some sort of a "Bible code," that Lewis meant for us to think of Josiah and only Josiah, and we have "missed it" until we do? No, certainly not. But do I think that Josiah as a character, embodying certain archetypes that are bigger than the historical man, was part of Lewis' symbolic vocabulary that he tapped into to create this figure? Yes, absolutely I believe that. Lewis was too literate and too biblically minded for the similarities to be purely coincidence. When writing a story of an ideal land ruled by kings, how could he not think of kings in the Bible, when, after all, the story is mostly about the King of kings from the Bible?