I'm not sure I understand your question. Are you asking if it is possible to claim to have musical knowledge/expertise without having a knowledge of classical music? If that is your question, I think the answer could be yes, but...

An awareness of the structure and form of classical music would provide information about so many of the basic parts of any type of music - rhythm, melody, counterpoint, structure of harmony, structure of musical compositions, and so on. I suppose one could learn these basics without illustrations from the classical world, but I think it would leave a significant hole in one's background.