You know, I actually really appreciate the "non-classical" aspect of this, because as has been pointed out, a good number of people who were actually alive at the time and were learning and playing the music were not professionals. So even if there was an "accepted method" of singing/playing it at the time, they weren't likely doing it "right", and that was perfectly fine.
I have been particularly looking for recordings of people singing medieval music without the "classical sound" because when attempting to do reenactment and things of that nature, it makes sense to learn how it actually would have been sung by everyday people rather than professional musicians and church choirs.
I absolutely don't think it's valid to say that he's singing it wrong or he shouldn't sing it because he's not trained that way, because if the only people allowed to sing and play music were the ones who were trained in specific ways, music of many types would simply die out.
I particularly find it an odd opinion on a site which is primarily dedicated to folk music, which, if you apply those rules to it, could never be performed.