New versions or re-makes

 I'm talking about films and tv here. It seems to be popular to re-make a program or movie. Over recent years we had the Starsky and Hutch movie, a CHIPS movie, a number of others,  various tv series.
 More recently we had the frankly bloody awful Ghostbusters just made to give women more staring roles, same with Oceans 8 (both box office flops).
 However a worse new trend is showing it's ugly head. A remake but changed from the original book (or film) the Classic updated to modern time Shakespeare for example.
 This week we had the ABC murders by the BBC, sadly they changed Hercule Poirot so much his own mother wouldn't recognize him. The problem here is they are changing parts of the story the author though was important and places a lot of emphasis on, like his accent and appearence.
 My question then is at what point does a story stop being the work it's claimed to be? in this case is it fair to call it Agatha Christie ABC murders? Or the ABC murders by the BBC?
 If I rewrite a Harry Potter film, but make Harry a Latvian refugee dwarf, who gets a chance to work at Hogwarts chip shop in Earls court road, and meets Hermione Granger, the barmaid of the Bell and Hammer pub and Ron a city banker. Can I really still call it Harry Potter by J. K. Rowling?  I have my doubts. 
 But the James Bond films do it, the last lot only have the title and Bond  in common with the books.
 That said if the Beeb see this they'll no doubt have someone writing the story as we speak...