We run a web content monitoring service, every media organisation changes their articles as they get new info. No reference is ever made to these changes. It's actually really interesting seeing how stories get updated.
Reading the cached article, and then going back to the original, I think it is fully within your duty to inform your readers that the article has been updated specifically for the reason of clarification and acknowledging a mistake was made, and that new information has come to the fore.
Trying to hide behind that by virtually rewriting the article is just unsavory, and I expect better from the BBC News.
Sorry if it seems like I'm taking a high road here, but I am; retroactive continuity has NO place in journalism.