More validity to whom though? I don't mean to argue with you over an issue this trivial, because I believe that what you are saying has a certain validity to it, but what I am trying to express is that I cannot see any justification for saying that it must be interpreted in a Christian context in order to be understood correctly.
Modern Christian interpretations were not developed in the early church (which was incredibly diverse, muddled, and unsure of itself), but in the 5th, 6th, and 7th centuries. Now, it seems perfectly reasonable from a purely agnostic point of view, to question the validity of Christian Dogma, using scripture from as objective approach as is possible. Christians themselves do not agree on interpretation. So, just because (and this is my main point) a person is not interpreting the Bible in a Christian context, doesn't mean that they are unable to objectively extract true meaning from the text - given linguistic, anthropological, and historical methods. I am not advocating "take whatever you want from the Bible - all opinions are equally valid".
Therefore, when you say that, "that any criticism which relies on a tradition alien to the faith being criticized is automatically going to have less validity than one made within the tradition of the faith criticized", what you are saying is that the tradition determines the interpretation, based on subjectivity. However, if the interpretation is subjective, how does it retain any special validity in any case for anyone? It's subjective.