I really don't care if they got it wrong or lied about it or whatever, I just watch it for the fights at the end.  The so called 'facts', as the term can be applied, can't really be 'proven' or otherwise no matter how you do the math because it's all based on FICTION.  So, I don't care about how accurate it is or isn't, I just enjoy the idea they'd bother to put so much effort into it in the first place.  So let's do the SENSIBLE thing and just enjoy the show for what it is, not try to take apart every little detail.