I just stumbled upon this post and decided to add my 2 cents..I too have seen a few illustrations of the match through the tube.
There is a local builder of matchlock's here in the SF Bay area, George Silva, who is a retired carpenter who built replica weapons for props at Paramount Studios; he has studied originals in museums around the globe and has spent countless hours conducting research. He told me that he believes that someone, somewhere, made a poor assumption that the site tube was for the match cord, and that this mistake has been perpetuated because some "expert" said that it was so. He also mentioned that he examined original weapons at the Metropolitan Museum in NY a few decades ago, and that they had one on display with a replica slow match in the tube because "a book showed it that way."