questioning such an apparition draws fire
Any alleged apparition happening among Catholics gets "questioned" quite thoroughly, and more often than not it gets rejected. By Catholics. If it gains any kind of following, the local Bishop (that's the office often translated as "overseer" in Protestant Bibles) gets involved, his word is considered final (because the authority and office he holds are from God) ... and his word is usually "NO". Far from drawing fire, we consider this inquisition normal, necessary, and laudable.
David can address how our brethren in the East handle such matters.
That Mary never physically left the Clositer suggests bilocation and the reality this happened is confirmed by many different events.
In any event, "The Lady in Blue" (The color of her Order's Habit) taught them the Gospel and they taught her how to make Chili. If that is not an example of a great cultural exchange,nothing is...