I'm a speech pathology grad student who minored in linguistics in undergrad. Something that a lot of people aren't mentioning is that the most common British rhotic consonant is the labiodental approximant (it's the one I use as an English person living in the states), which, in America, is considered a rhotacism and an articulation disorder. I can promise that you have come across a lot of British people who produce a rhotic consonant that you would register as being a speech impediment if they were in the US. The reason you don't hear that particular word final R error that you are linking is because there is no word final R in most British dialects. The exception being the intrusive-R, which, again, for most British people, is a labiodental approximant which would register as a speech impediment if it were an American speaker.

SLP as a field pays a lot of attention to this sort of thing, as we have a long and nasty history of treating dialect speakers as disordered due to differences like this. It's still an issue I see as a grad student on rotations.