Even if we did not have any understanding of the neurology, I'm not sure why pointing to an empirical record of successful face recognition shouldn't be fairly convincing. Is the point that we could be lying about our record?

(In the specific example given, you could probably get a fair bit of mileage from explaining the nature of vision, even without the specifics of face-recognition. I'm not really sure what broader lesson that might have though, as I don't fully understand the nature of the question you're asking.)