they used historic footage of the Peking, a very common thing in documentaries and completely legitimate

and many of your points were actually brought out in the video, which I am fairly certain you never bothered to watch...

they even had a short segment on a coastal village with a tradition of maritime hymns - something that the late, great Lou/Louisa Killen talked about when performing The Rose in June at Mystic Seaport.

I don't know a dang thing about Mr. Malone, but I have been involved in the study of shanties and sea songs for fifty years, along with the various efforts to preserve them... and this BBC effort is a worthwhile watch and I hope you and others will take the opportunity to view it...